Statistics Lecture 4.2: Introduction to Probability

all right so talking about probability again this is our transition between from descriptive statistics into inferential so we're talking about probabilities is chapter four like I said is the basis for making decisions about our data that it's really what we're doing and it's based on this idea if something has a low probability that means its occurrence is going to be rare so if something has a low chance of happening you say it's probably not going to happen that that's really the whole idea here I mean it might be an obvious statement but what we're going to think of it is low probability means rare or unusual occurrences occurrences two hours one hour I never know I think it's too like that one is this occurrence is okay one hour you are right and here's some vocabulary that we do need to talk about speaking of vocabulary there's some vocabulary that we need to talk about as well before we get going on exactly what probability is going to be in relation to this class the first we're going to talk about is a word called an event event in statistics doesn't mean event like in English in English an event means you're having like a party or something that's already vent here that's not what it means what event means for us is a collection of outcomes of a procedure so an event is what you get from a procedure I'll explain this in give you examples in just a minute so event it's a collection of outcomes of a procedure so something you're doing we also have another couple words we have something called a simple prevent a simple event is a single outcome one specific single outcome don't worry I'm going to flesh all of this out with an example in about two or three minutes last word we have something called a sample space the sample space is everything that could possibly happen all the simple events so all simple events in other words every possible outcome so any event if that is something that could happen when you do a procedure procedure such as willing to die flipping a coin so they'd involve some chance in their a simple event is one specific outcome that you can get the sample space is everything that you can possibly get from flipping the coin or willing to die so let me give you example we'll talk about flipping a coin and we will identify some events and some simple events and then the sample space would you like to do that we kind of get an idea but what this up actually means so let's go ahead and our example would be flipping a coin so our procedure we're going to flip the coin one time so you can take a coin out of your pocket you're going to flip it and you're done the others have the procedure right here's an example of an event an event could be what can you get out of the coin can you get edge easily if you would it be cool if you just flipped it in land on the edge sure happening before has ever happened I wonder if it's happened to somebody before well they've been like a edge of a coin it's like that why they can probably happen but like with a quarter or something it's really rare that that's ever going to happen that I don't know that ever has anyway that's just four possibility I guess but if you're flipping a coin there's only two things that can happen right you can get heads or tails when you're talking about an event you're specifying one thing that could happen and what you're looking for so an example of an event in this case would be you're looking to four how many heads you get so an event an example of event would be head look at it which coincidentally that's also a supplement one thing that can happen our sample space includes every possible outcome you can get when you do your procedure now our procedure to slip in a coin how many times just once so you flip the coin what could you possibly get from flipping the coin one time okay so that's what our simple our sample space is as you either get a head or you get a tail can you get anything else besides a head or a tail when you flip the coin one time now we're not going to get through the edge thing that's really not realistic and we put these funny little brackets around there if you're trying for the first time that might end up like that that's okay it's a nice curvy bracket metal takes you a lot of years to master that master's-level stuff you know five brackets so our sample space is a collection of simple events so here's what we're talking about procedure is what your you're doing event is what you're looking for simple events are what could happen and your sample space is a collection of all those things you kind understand more the idea of events simple events and sample spaces the next example will really make it even more clear for you so the procedures what you're doing the event is one outcome that you're looking for so we're looking to get for a head here or you could append tails there what you can get a flip by flip those are called your simple events one out one specific outcome so here we can only get a head or tail if you combine all of those simple events together you get what's called to our sample space now if you're so with me on this let's do one more example to really illustrate this the procedure now is we're going to take that coin back in our pocket we're going to flip it three times so we're going to flip over that be thrice on foot price three times if you flip the coin three times what could you get well you get heads or tails for the first one right but then you flip it again what could you get it that one okay then you flip it again we should get up so an event is like this and that says what what possible combinations could you have those would be considered our events so one event would be I'm looking for one head and two tails that's an example of an event one specific outcome of your your procedure does that make sense to you so this says okay one thing that could happen here is I get a head and two tails now we're going to find out each of the simple events so what are the simple events that could happen what could you get when you flip your coin three times you could get three heads that's a good place to start so you get all three heads Hey what else could you get but you get tell sometimes okay that thing but that down here that could happen right these right now we're finding these are simple events they're single outcomes that we can get from flipping the coin three times can we get just a single head not if you well I'm sorry can you get just a single head and no tails not even flipping it three times right you're going to get three distinct things that happen a head and a tail tail a tail what else could I get okay so I heard two kids at would we need two heads in one table sounds a little weird I mean in order like you can get two heads in a tail several different ways one way could be if you go head and tail right give me another way head tail head that's another Google okay what about another one anything else that we could do starting with heads well you know what that was mean certainly heads anything we could do I'm going to race excited starting with heads we have Edvin head head tail head tail head head so these are all this all simple let's start with heads we can do head head head head head tail head tail head head tail tail let's do the tail ones we could have tail tail tail give me some other things that we could have here tail tail one up you could have tail head head you could have tail tail head tail head tail and we only have a tail tail tail would you look that over did I miss any did I miss any possible outcomes we could get are you seeing how we're getting these things we're just imagining flipping a coin right imagine flipping the coin three times you can get head head head you get ahead ahead in the tail it's easiest to do it that way look for me to sit there and think of all the heads and to think of all the ways you have a head first we head head head great head and then tail or head and then the tail in the head or a head and then two tails and that takes care of everything it starts a page then you go tail tail tail tail tail with an H then tail and a head tail tail and that way you know you have all of them up there you with me okay so what we've just done we've listed out all the possible single outcomes up here you with me on that all the possible single outcomes those are all the simple events simple events mean a single outcome so what we've done here that's a simple event that's a simple event and so are the rest of these all eight of these things are called simple events if I group them all together like I've done what we have is called the sample space the sample space is a collection of everything that could possibly happen bridging out you're with me on that now let me because the biggest thing for people is like well what's the difference parents implement and an event isn't event the same thing the answer's no an event is it doesn't matter how you get it that's what I'm looking for so for instance our procedures flipping ahead or flipping a coin three times our event we're looking for is getting one head and two tails that's one of the things that we could get flipping the coin three times right this is one of the things that you get here is all of our possible simple events or our sample space or each individual outcome those things are kind of synonymous but the collection of simple events is the sample space how many ways can this happen is there more than one way you can get one head and two tails how many ways hey six wins one head two tails does this have one head and two tails two nails does this have one head and two tails oh this one's one head to get out of this one that's one of them a little star there this one this one one head two tails this this one has two dads one time so here's the difference between an event and simplement an event says overall what are you looking to have happen but you're looking for ahead and two days simple events are the way that you can accomplish that event are you seeing the difference the event is what you're looking for simple events are ways you could accomplish that or not accomplish that they're all the specific outcomes so how many ways can we accomplish our event there's three ways three simple events will compass our main event does that make sense to you so it's a little little tricked up gs have any question at all it's a little tricky sometimes if you really don't get the the whole concept so are there any questions on what we just talked about procedure that's kind of basic that's just what you're doing events are what you're looking for simple events are how you accomplish your events there are individual outcomes some of them are going to accomplish your events some of them obviously are not going to accomplish your events let's try one more I want you to do it give me another event that I can add with flipping a coin three times it's another bad what could happen or you can anything else happened besides one head in two tails okay give you one what no one tail one tail two heads okay is there any other events that I could have what's that three days how many tails well not because all it is and the last one we could have is what so these are all examples of events we have here's an event here's another event these are the last two events there's really nothing else could happen right notice how many individual items we have so there's more individual outcomes than we have total events because some of these overlap this right here that I starred that's three ways to accomplish this one event how many ways can you accomplish this event can you see it how many ways where are we finding that out look over there how many how many times do you get one tail and two heads here's one tail and two heads that's extreme one here's one hit Taylor two heads there's another one that's one two three sweetly things that's Kali things so the three sweetly things that accomplishes this event three single outcomes three simple events would accomplish this event true okay how many ways can you accomplish this event there's only one property date how do you think does this one and circle name is that one I'm just rounding I mean this this is the relationship between simple events and events events are the overall thing you're looking for okay that's it simple events are the individual outcomes that you could get from your procedure some of those simple events are going to satisfy your event maybe only one may be up to three maybe more than that if we were flipping a coin four times you have lots of outcomes that satisfy your event do you understand relationship between procedures events and simple events and sample space sample space another problems to collect all individual civil outcomes and that's or supplemented so now that we understand that we can really use those words to kind of describe some probabilities so let's do that right now when we say probability in this class we save possibility we're talking about the likelihood of an event occurring the likelihood of an event occurring notice I'm not saying the likelihood of a simple event although sometimes those might be one of the same if there's only one possible outcome that satisfies your event then the probability is one the same but when we talk about probability we're saying the probability that your event happens or the likelihood the likelihood of an event occurring we're going to use what letter do you think we use for probability geniuses every one of you what it was like our one should be confused no be you're exactly right so probability is P events are usually listed with capital letters so if we're talking about event a we're just going to say a so a could be flipping a coin three times and then whatever you're talking about so we can list it you can even list it in words you don't have to use the letters but if we're talking about an event so for instance event a or you could write flipping a coin three times over anything like this BC etc if we're talking about the probability of an event occurring the way we write that as we say probability of a that doesn't mean multiplication it's not like algebra it says probability of a it's more like a function notation if you want to consider into something you're finding the probability of this event happening basically and so this means the probability of event a actually occurring now when you talk about probability we actually have types of probability we deal with and you deal with this on a day to day basis I really you do when you think about it you'll probably notice this when I'm going through it but there are three types of probability the first type of probability is what you get when you actually perform an experiment it's called observed probability so observe probability happens when like you took your coin and you flipped it a hundred times and you calculate how many heads you got and cousin how many tails you got from there you can actually mathematically figure out what's the probability of getting a head cuz maybe your coins waiting a little funny do you see the Olympics right there that's observed probability when you actually do something and you get a probability from that observation you follow so observe probability its probability that is estimated based on your observation probability that is estimated an estimated wait a second why estimated why isn't the exact can you ever do a procedure for so long that you that you've accomplished all empresa different way that is emitting is inflow right can you ever perform a procedure so many times that you've exhausted all the possible times you can do it for instance could you flip a coin until you can stop flipping it claiming work can you do that forever so can you calculate the probability if you can't do it forever exactly the answer's no you can't flip a coin enough for you to have an exact probability all you can do is say maybe I flip it 100,000 times is that enough to get the probability of flipping the coin answers pretty close but no not exactly I mean you're not going to get the exact probability of flipping a coin by doing observations one that's what's called observed it's estimated you observe it for a certain number that you decide on say I will flip the coin 100 times and after that I'm going to calculate the probability to be estimated it's not gonna be exact because I can't flip that coin forever I don't want to trip up in a certain number of times to make sure that I have at least a good sample of outcomes there does that make sense so we can do it forever that's why it's estimated and fortunately it's not too hard to figure out if we want to find the probability of a here all we do is we take the number of times a occur divided by the number of times you perform that procedure so number of times a occurred over a is your event number of times they occurred just divided by the number of times your procedure was repeated so the number of times you did that thing I'm going to give you all three of these and then we're going to give some examples so we can calculate these things so first what observe its you're actually doing something you're actually going out there and flipping the coin or going out there and taking a poll or going out there observing what someone's doing and that's your basic probability off of that okay a perfect example for this if you really want to right now so you're not really quite clear is too much baseball do you know what baseball is okay so you know these guys up there with the sticks they swing right if this is a white thing coming ten all right sometimes it hits them and they get mad they got hustle hustle haven't earned that while they tussle a little bit so baseball is all about statistics right I'm here statistics on baseball players all the time if you're into sports or you watch sports center for like five minutes are always talking about baseball at person handling baseball but if you play whatever that's cool so but they're always talking about the statistics and so if someone has a batting average of 100 would you expect them to go through the ball do you think that an average of 100 means one out of every ten ten times they're going to hit the ball is that good is that bad a batting average of 400 is excellent okay bad average of 100 really sucks it's they're not getting them all but that that right there with they're getting that batting average of 400 or 450 or 333 any of those those decimals that you see on the back of a baseball court if they're talking about that that is an absurd thing right what they did is they said oh how many times have you hit the ball eight times how many times are you up to bat 24 that means that eight times out of 24 times you hit the ball that's 33% four point three three three that's how they're calculating that that would be an observed probability because later on they're gonna say oh you usually hit the ball eight times out of every twenty four times right are you automatically going to be coming that's huge success in it every single time maybe but probably not probably you're going to stick with those odds that's observed probability and how you use it does that make sense to you so it's what someone's actually done and then you take that and you estimate it and you apply it towards towards their future say if you hit the ball eight times out of every twenty four times chances are you're going to probably continue that statistic so when you come up with that next you get a one-third chance of hitting the ball that's how you use observed probability letter if you're armed with that so observed is something actually happened you measured it the next one is classful probability the next one is what I say to you and you answer me this question I say what's the probability of flipping a coin and getting ahead okay you have to answer to play along here what's the what's the probability of you flipping a coin and getting ahead obviously right there's two choices one of those switches is ahead so you 50% right what's the probability of willing to die at one time and getting a to fly one out of six and how many choices are toons that's how you didn't want on six right that is classical probability are you actually rolling the die to figure that out your head you're just thinking about it right you're thinking oh obviously there's six sides only one of them's a two so a one in six chance you're doing classical probability there notice the difference between observed where they actually calculated how many times you hit the ball divided by how many times is up to classical classical is a theory observed probability is the actuality the classical is what should been observed is what did happen do you see the difference theory classical is what should happen when you flip the coin you should get half heads half tails if you flip a coin ten times are you gonna for sure get five heads and five tails if you think so I'll make you a bet right now and make a lot of money with you that I can flip the coin rarely is it going to be exactly five heads rarely you're rarely going to get that I mean well not very many figures of the time a lot of money from you if we make that bet every single time over it over again so you're not going to get exactly five heads every single time the second happen sometimes you'll get six heads out and sometimes you get nine Spears equal ten sometimes get one but that's okay that's the that's a classical probability as opposed to the observed classical is what should happen every time observe is if you actually do the experiment what does happen every time so let's talk about classical we can pretty much just discuss dude this is the probability based on the chance of something occurring this is this is a theory like the theory aspect of photo by the way for classical probability to work each event has to have an equal chance of occurring inch simple event has to have an equal chance of occurring make an example about this okay let's say that you had because this statement people are like well why why does it have to have an equal chance memory think about that so let me give you a die and I'll tell you it's a way to die okay it's a way to die what's the problem zero weighted diets but die in a corner so it comes out certain numbers differently using the Vegas sometime of the use to his seventh all the time I haven't ever do anything like that the simple event you must have an equal chance McCurry means that if I give you a way to die and I say what's probably going to you can't say one sixth anymore because well you don't know you don't know what the weight is so in order for you to do the theory approach to something that has a chance of occurring you have to have an equal chance there right the only way you were able to figure out one sixth earlier when I said what's probably going to is because you thought that every side has an equal chance of happening right that's why you did that that's why when you said well it gets ahead fifty percent of time when you put the coin once because you figure heads and tails has an equal shot don't you that's what classical is based on it's based on every simple bit that's an equal chance Maternity now the way that we did this you've already done it you know classical probability intuitively that's when we talk about most of time looks really similar it's just that instead of number of times a occurred we say the number of times a could occur or a number of ways I guess divided by the total number of possible outcomes again it's a number of simple events and we just mean how comes there because we've kind of covered that at length right now I need to recap this a little bit before we go any further so you really need to understand the difference between observed probability and classical I'm going to ask you on your test would give you a problem saying what is this calculating probability tell me if it's observed for class well that's going to be like three or four files on your test so you need to be able to identify are you doing something or are you just thinking about it that's the difference if you're observing something or someone has observed something that's observed probability if you're thinking about how many times could you get a - if I'm willing to die if it's something like that where you're actually not doing anything you're just thinking about doing something that's the classical so what right up here is observed and classically this is what could happen this is what did happen you know what let me replace could would should this is what should happen not good this is what should happen this is what you did happen let's not only use example but if you flip the coin 10 times what should you get you should get five heads five tails if you actually did it are you going to get five head spot tails maybe maybe not if you do the observation you might get six heads and for tails that's what did happen so that's the difference you can do the same you can think about the the probability it should be five out of ten you can do the probability it might not be private of ten those things could line up but they don't have to put the act of doing that procedure that's observed accompanying it that you're just thinking about it and figuring out what should what should be events the class will humble understand the difference okay the last thing we have to have to talk about is called subjective probability now before you say well that has no place in statistics why real and subjective probability that's subjective when you've been talking this voice electives some very well subjective puggly is something we do every single day you go to your doctor and you go doctor what are the chances I'm going to make it and he goes 80% does that mean out of every 10 people that he's worked on two of them died you know it just means his best guess for your particular situation is get a pretty good shot to make it it don't worry about it 8% pretty good right 20% only one shot on the fight that you're gonna clever you know we take chances but anyway that's subjective probability how about this one one of the chances right now that I'm going to walk out that door you might want this to happen but my walk out the door get hit by meteor no you won't want that on me with you because you probably take it with me because we're a safe building so if I walk out the door or the chances I'm gonna get hit by a meteor 90 percent probably not um how many to lose it huh I mean is it zero is there a chance any point zero zero zero forever in the little one and maybe but the point is that it's neither classical notes of jet subjected I'm not thinking in my head how many possible ways could I walk outside New Year right now well I'm not thinking I'm going to calculate how many ways I've walked out of this classroom and then how many times I've got hit by meteor and figure out what the percentage is right that's not what I'm doing this is not an observation I haven't walked out this time a million a room a million times and calculated all I've got in my meteor zero therefore the probability is zero there is a chance it's a very small chance but it's a subjective chance I'm just kind of making it up right best on based on my past experience and based on my educated guess it hasn't happened to me before I know that meteor circle around but none of them has ever even come close to me so it's probably close to zero but it's not based on any map it's not classical it's not sort of sheet of difference the doctor thinks probably the best one he's not basing that on map he's not doing the calculations you saying out there you got like a 95% chance of being okay or you get a 20% chance this is going to turn into cancer or something I mean that that happens all the time but people say that so that's the subjective type of probability it's someone's estimate based on an educated guess now let's go ahead and do some examples here and see what we can find out about these things whether they're classical or observe and then we'll calculate the probabilities as we go okay so first one the probability of selecting a part art like that like that not like the feeding heart under the heart shape from a standard deck of cards if they're shuffled up and everything random selecting so someone holds up genome cards some people invited it on and familiar with the cards cards have more suits diamonds spades clubs hearts there's 13 of each suit ok so there's 13 cards of certain clubs that can spades 13 whatever I did say and there's 52 total cards right cards are labeled 2 through 10 then you have Jack Queen King and ace making up 13 individual numbers for each suit of cards if you're not familiar with cards do some packet cards because I'm going to use that some of our tests to illustrate this so probably select a heart from a standard deck of cards so we want the probability of art let's find u symbols like that that's okay we don't have to call it event a in this class we say we want the probability of finding a heart I don't mean true love just kidding just kidding filter love congratulations I better not have a girlfriend watch this video so anyway we're going to count the number of parts there are divided by the number of total cards there are so how many parts do you have in the deck Hardison okay and how many Bogart's calculate probability how much is that would you get 0.25 cool which is actually the probability of finding true love in the real world that's courtesy I mean weird even the thing anyway so yeah there's a 25% chance of finding true love or a heart in a deck now is this classical or observed probability what you think did you actually go pull the card out of the deck then it's not served okay did you actually pull the card out of the deck did anyone pull the card out of the deck then you would talk about pulling several cards other deck can calculate no what you did is you said how many is there divided by how many total cards there are what should happen you should have a 25% shot but pulling out a heart from that day that's classical probability are you always saying that this is classful okay this is what should happen now let's say this last example for today you take a coin you flip a coin 100 times you happen to get 64 tails what I want to know is what's the probability of getting a tail find the positive in your tail here's how we do this with with observed or classically the one you find out the number of possible things you had so in our case how many times did we actually flip the coin how many tails did we find well this shouldn't be too hard to figure out what's probability there once you say here's you have a 64 percent chance of getting a tail now is this classical or just observed did anyone actually flip the coin yes they did that's absolutely definitely absurd because look at the difference here here it says you flip the coin 100 times you get 64 tails someone actually did that okay so it did something here didn't even do anything that's theory this is this is observed this is what actually happens so what this is the observed it's what did happen first objective use the doctor one yeah eh percent chance of being okay how many wanna show we've talked to us man okay I'll just show you my true love it does exist it's making a funny okay so we go home let's start crying or anything it's okay so as we're talking about last time we did some examples of how to do observe classical and subjective probability let's continue that so if you didn't know my favorite quarterback - unfortunately playing anymore I guess is Peyton Manning you know pignetti yeah right his neck or some digging out to see if he was just a real man just play with a neck injury and it's smart to do right yeah yeah yeah no I'm just kidding you never want to mess with nature so I've heard I guess it's important so next couple things anyway Pigman II when he first started elf I'm making a statistic up but he's pretty good so it's probably true completed 385 out of his first 528 passes what I want to know is find the probability that Peyton Manning's going to complete the pass using this information okay let's talk a little bit about the vocabulary of the statistic stuff is probability that we were talking about firstly can you tell me what the event is here what's the event what are we looking to have happen because that's our effect not just a pass or what about the pass okay completing the pass would be the event we're looking for what's the procedure listen what's happening here yes that's right that's the procedure he's actually throwing the ball to somebody that's a procedure the event is we're looking to see if he's going to complete a pass that's what we want to find out you guys okay on those those two things so procedures what's happening event is what we're looking to see find the probability of action encouraged so our men is concluding a pass by the way what letter stands for probability is where you use that's pretty clear so probability we're just going to write the event completing a pass now a lot of people if I ask them it or if you went on the street you said um can you tell me what's the probability of Peyton Manning completed paths this would be the same idea as if you win outside and ask some people really don't understand probability once a project is going to rain today and they say oh well 50% it's going to be 50% with this you completely completely pass or not because either he's going to complete it or he's not either it's going to rain or it's not that type of logic you see how that's kind of like false logic for what we're talking about that there's a whole bunch that goes into calculating whether it's going to rain or not today probably it's not gonna rain I'm not I'm thinking it's probably not fifty-fifty like is in a brain like half the time all the time that happen to make sense we know if it's like July 20th what's the probability it's gonna rain on July 20th in the Central Valley pretty close to zero yes what's the probability Peyton Manning's going to complete a pass well it's not 50/50 because he doesn't complete exactly 50 percent of his passes it ordered makes such a judgment you actually have to consider his past practices what he's been doing so that's where this information is going to come in you can't just arbitrarily say a percentage that would then not be classical or observed probability that would be subjective probability based on actually not an educated guess based on you not understanding the probability so I need to to kind of get away from the thought of if it happens or it doesn't happen that's automatically 50/50 to see how that's not always the case you sure okay well it'd be like this what's the probability I'm going to wear a dress tomorrow it's not fifty fifty bucks it is zero I mean 100 I mean zero it's Tuesday you don't know what I do on Tuesdays so what so I'm just joking I don't wear dresses only on Halloween once yeah that's the last day yeah take them over okay so instead of just going fall it's 5050 we're going to use information than I've given us and how again the probability is we calculated the number of times something actually happened successfully the number of times our event occurs that's what the more specific way to say that the number of times our event occurred divided by the number of times the procedure was repeated so how many times did our event occur here which was completed a pass right how many times did was the procedure repeated right when you're doing the probability give me three decimal places because we like to translate that to a percentage often and we want to make sure we have like 35 points something percent that's comedy what is it like that route it trickling yes only 70 knots point 79 then so 72 point nine percent so this or or that is that good now that's a judgment call right and when this was actually just calculating probability saying whether that's good or not that's a judgement call you say oh well that's good or that's not good what if someone completes 100% pass all the time then relatively he would be as good but 73 percent is pretty good for completing passes so lately are you guys all okay with them with actually calculating this probability now the question I have for you what you also need to know this is the problem like this is going to be directly under test just like that but then there's going to be a Part B and you have to answer whether this is don't say it out loud and what the people think about it whether this is classical or observed probability so think on that for a second is it classical or observed or subjective and here's the differences again to show you you kind of get this in your head subjective means there's no data whatsoever you just are making something up but it's based on educated guess like a doctor would when a doctor says you have a 90% chance of pulling through that would be subject subjected classical would be based on the theory like what should happen in this procedure or this for our outcomes observed is something actually happened you calculated it based on past incidents incidences of occurrence or past procedures so using that information is this observed is this classical or is this subjective definitely observe he actually threw the ball right if she did something that someone just wrote down every time what happen that is observed there'd be no way to do this classically because well really I mean if you think about it in order for you to do a classical probability the outcome has to have the same chance of success every time right every single time and we Peyton Manning throws the football sometimes it's like from you and sometimes it's from here 280 yards down the field this guy's got a rocket laser rocket arm I've seen commercial nobody this is like eight years ago I'm older than I get so anyway he's got a laser rocket on so you know so anyway he throws the ball there's there's less chest of that actually succeeding you can't calculate the chances every single time we can't even do this classically it's the only way we can do it is observed let's look at a couple more let's say I give you a deck card to help you guys loop through the deck of cards yet gets removed with the deck of cards hopefully your so given a standard random deck of cards let's find the probability of randomly selecting a two so we want to find here's how you would write yourself the probability of - what's our event in this case see that letter that's the event what's the procedure procedure what are you actually doing or you pretend you to do I guess your guinea pig in the card that's procedure pick out one card the event would be we're looking to see you what's probability find the to doesn't get between a procedure and it event okay so if we're going to do this we need to have the number of choices that are going to make our event successful or we're going to over the number of choices that we have total so what are the total number of choices we have four cards in a standard deck of cards now how many ways can we accomplish our event four ways or what is yeah because there's one two in each suit so that's four and we calculate 4 out of 52 now which is 4 out of 52 point 0 7 how much is that as a percent yeah is that good or bad let's get subjective right here I mean for you that might be low that's a fairly low probability of getting the two randomly out of 52 cards not like 50% searching about 73% like peyton manning doing football it's like a sure thing but random deck of cards you're selecting the tube now is this subjective probability I'll be just guessing you so definitely up that is it observed probability or is it classical what do you think why isn't it observed we can actually go through the motion of taking the cards out and say no we got it to put it aside I'll keep going up you got another two right you didn't you've yet you didn't do it at all it's not like big many right he actually threw the ball and you calculated that you didn't say oh I drew a card out and put it back eighty-three times and out of those eighty-three times twenty one of them or twos or something like that or five of them or two you didn't actually do a procedure here you just calculated the what should happen in your procedure did you see the difference here between the big man example where he actually did something in this example now could you turn a card example into an actual observed probability answer sure you could if you just took a deck of cards and did it you know so if I gave you this on a test and said okay a person drew out five cards with replacement from a deck of cards he got one two a jack a king another to ten ace what's the probability they're going to that you are going to pull out a 2 from this deck of cards you know you had two 2s and pulled out out of 52 cards that would be I'm sorry out of five tries so that would be your probability is the two out of five so it'd be how much you got out of how many cards you drew does that make sense to you okay so that's that's the difference here you can talk about the same question it depends on how this was actually accomplished whether they did the procedure over the top of the theory of it so this for sure for us this is going to be classical you know a while back someone did a poll on cloning back when stem-cell research was just kind of coming out of this a few years ago and stem cells people thought they're going to be using those from cloning and so they did this this poll on whether people thought cloning cloning people was good or bad so here's the results of that huh-huh so when they did this poll 91 percent I'm sorry about 9 1 % 91 people said cloning was really good idea because they wanted this extra person I mean she seen the I have you seen the movie the island great movie I'll kinda bout the cloning idea all I don't want to ruin it for you but it's about this ruin it for you 91 people said cloning was a really good thing Tony good 901 people say you know why does not run so sure about this cloning thing say cloning back the rest of the people had no opinion and because you're always going to get some no opinions in a group like in whatever little cares open the video games and you know so 20 people now maybe they should know they really don't have the information haven't really thought about that then you have the opinion if this was a random poll this should give us some indication about the general public whether you can go outside right now and ask somebody about cloning whether they think it's a good or a bad idea this was collected randomly in the methods that we've used or in his class remember talking about those like a systematic sampling or the stratified or the cluster sampling all that good stuff so let's pretend this was done that way maybe it was I really don't remember where this came from let's say it was it should give us some indication about everyday people so let's go ahead and find the probability that we can go outside right now and randomly select a person who thinks cloning is a good idea so we want to find we're going to use appropriate symbols here we want to find a probability that someone thinks cloning is good how in the world are we gonna figure this out how in the world firstly before being talk about that can we determine whether this is classical or observed or subjective is a subjective its objective now it's based on some data here so is this going to be classical or is it going to be the serve what do you think it's based on some something that actually happened right it's people went out there click the data polls hopefully this is polls open up polls are always observed because you're always collecting data right you're always talking to somebody that's that's observed you're observing what they're they're doing it's not classical is not based on theory it's what actually you collected so a poll is definitely always going to be inserted so write that down this is certainly observed probability holding the attention observed at classical is becoming really clear to you I hope that's happening now how do we calculate observed probability well it certainly is still division because it's our saw village are calculated we calculate the number of people a number of things that accomplish our event divided by the number of times a procedure was repeated so number of times that we accomplished our event which was cloning was good honey is that how much zidler anymore very good Cloney good feeling good now you want people many more people out of how many people wouldn't have to do find how many people is out of 91 is out 901 add them up add up these two good because even though nobody opinion people they still took that poll right they just didn't categorize themselves so we add all that up what up I got sweet that's how many people were involved in this poll in this procedure so we calculate 91 divided by our 1012 and to the third decimal place we get what is it point zero eight nine nine good the nine moves that nine up to a ten but it okay good it's basically nine percent so right now going out there is what this suggests is that randomly picking out a person you should have a nine percent probability of being somebody thinks calling this good thing so maybe that's higher now who really knows but this is oh this is an old poll that's how you would calculate such things which originally feel good what we talked about so far okay good that's fantastic are there any questions before you go on I have to race this side here yelling can't understand the whole peyton manning thing and some server because he actually did the passes the deck of cards we're not really drawn cards just kind of thinking about what should happen here that's our classical we have another observe any time you did a poll man but if they're doing the research that's definitely observed they're taking that information in hmm there you go find them find the probability that bird will poop on your car today if you wash your car and it happens right out there right up in the frigging are birds which other BB gun everybody anyway so find probably a virgin poop on your car today is that going to be a classical probability we're going to find it we think is there a way to tell how many ways this event can happen to me how many ways can spur poop on your car know everything flying it could like land the car get hit the windshield mule oh crap okay is it observed I mean you could you could talk about observed right if you had calculated how many times Birds had pooped on your car over the past whatever amount of days divided by number of days you have a probability there that would work have we done that so it's definitely a classical that's impossible because they all have an equal chance of the bird poop in your car every single day does it happen but what's it in the garage bird fruits on there I mean the unlucky that's really crazy it's happened me before actually bird was in my garage bird is on a berry anyway it's definitely not observed because we haven't really calculated this so the probability of a bird poop in your car is what is it for you whether it is subjected by me what's your probability for your car today would you say like ten percent sure that good thing I just put words in your mouth okay nobody ok what's the probably million Korean assumption not someone like that some some birds gonna undercard what would you think see for me it'd be like 50% we've done that's another thing about subjective right it can change person to person so if you can think of the probabilities and you say well for me that's 20% maybe your car never gets pooped on just like 5% for me it's like 50 to 70% always get some I'd park and retreat so I mean duh it's going to happen but subjective probabilities can do that right they can change can classical observe change now this is based on hard evidence this one was based on complete theory with jiton is not going to change okay so that's another way to kind of do this as well so find it probability this is stupid birds you know picked up in a car it's a it depends on who you are but this is certainly going to be subjective and it probably depends on where you are if you're partnered by the beach and there's lots of seagulls that yeah okay let's go ahead and do one more I'll give you a couple couple notes that are important for us and we'll continue to talk about some complimentary events what that even means let's find the probability that if a couple has three kids two of them are going to be voice now I also have to tell you that we're going to assume that the probability of a boy or girl coming out is 50% all right this is equal that's not always the case actually you actually do the observed probability girls right now have a higher chance of being born so that's I think there's like 51 percent women born 50 49 percent or something like that it's not exactly 50/50 but we're going to consider it for this exercise to be even is that make sense for you so assuming equal chance of moral some people chance for you to roll hey what firstly is our event having a kid first thing how many babies have you had we haven't just one can we ask the question if you have one baby how many ways can you get two boys if you have one baby and you cut them in half you guys are sick okay so firstly what is our procedure even what's our procedure what's happening here but now you can say it if you're wrong doesn't matter just you video recorded that when the world's going to hear it that's here so what is our procedure what are these people doing then making babies having babies making babies would be a different class so how many babies are there having I think one thing is only three that's our procedure the procedure is having three children deposition for cheezer's not just having babies it's having specific number of babies do you see the difference there you can't even talk about this if you only have one baby because you can't say out of having three children how many ways you have two voids if you're only having one baby you go within the category so our procedure right here you want to write that down the procedure is having three children now the event is based on that procedure what's the event the event is what you're looking for what are you looking for - two widow two bullets two boys and what else hopefully hopefully you get a girl and the f3 key I mean you're not just gonna get two boys or and nothing right ghouls count two guys well if you have two boys what's the other one primero a girl we hope it's going to be a girl so we have two boys and we have one girl we're not going to get three boys that would not be our bet so right here I guess I will write this down for you the procedure is having three children congratulations adding three children the event is getting two boys if I say two boys that means out of three children one has to be girls so we want to find the procedure I'm sorry the probability I'm sorry of our event two boys one girl oh my we have some other other words that we haven't talked about in a couple days now before we do that I do want to figure out whether this is going to be subjective observed or classical probability is it's going to be subjective probability we're going to be calculating stuff over here we're not just going 30% now we're not doing that right we're not basing it on it guess we're not a doctor we're going to be doing the actual either theory or observations here have we observed some people have we have served some people is this what we're doing do I have some data on the board or unit says here are 100 couples who have had three kids thirty of them have two boys have I done that so is this observed or classical do you think also this gives it away equal chance of being a boy-girl because in order to calculate the probability if it's classical you have to have the equal chance of something happening you can't do classical probability if you don't have that case okay if girls had a 51% chance of being born and boys only on 29% chance being born you couldn't do this classically okay you would have to do observe they have to have the equal chance like willing to die member talking about willing to die last time said it's a way to die all bets are off you can't do classical probability because it's not even you don't have an even chance of getting a one two three four five or six one reason you were able to come up with the last time as I said I said what's the probability of rolling a two you said L bones one six there's one two there's 6 sides therefore 1/6 that assumes that every side has an equal chance of coming up if that doesn't happen ie if this does not take place not equal you can't do this classically not going to understand that good now so we have our procedure we have our event we know this is going to be classical probability write that down if you want to this is certainly classical it is not observed we need to find out something called O or to find out what could happen what could happen is a whole group of outcomes is called our this is called fill so a full group outcomes everything that could happen all put together is called are see the low sample space does that weird ring a bell to you the sample space is every possible outcome you could get we need to list our sample space in order to do this classically because they have to know what can happen if you're willing to die your sample space is just easy it's one two three four five or six for this case though we're going to have some different different pens we have so the couple has three kids sample spaces have those funny-looking brackets let's list out what you get for three kids what's the person you could get or what's one thing you what should we start with I should soon all three boys okay great good boy then a boy then will with us okay good luck with that one what do you think it'd be tougher three boys two girls I think the girls would yeah personally boys are are just nasty gross people but girls can eat meat okay so three boys three girls what else could we get by the way I like to start off with this way and this way and then list out everything that starts with B everything certainty that way you don't forget anything so let's start with the two boys we got a bet we read that up there what's the next thing we could do that someone else give me another one okay give me another one boy girl girl anything else starting with a B no that's all okay so girls we need to do the girl girl boy we could do G B G and we can do gtp what have we missed it now before you start saying well mr. Leonard I mean aren't some of these the same like isn't wouldn't this be the same having two girls in one boy and then having a girl and boy a girl and no people I mean we have individual personalities right these are different people so if you had a girl first and then another girl and then a boy you'd have a different family than if you had your girl and then your boy then your girl wouldn't you completely family so these are eight different families that could happen with your situation if you're going to have three kids you with me on this okay so there is a difference there so if we have these eight different choices what we need to find out there's only eight different choices eight possible ways you can have three kids you agree with that right there's only eight possible ways all three boys and then all three girls and whatever you have permutation of those how many ways would accomplish our event which ones that's what I asked for oh this one very good yeah anything that has the two boys and the one girl because we didn't say what order right we just said ultimately to bottom row there's three ways that make it happen notice how it's certain I observed right we didn't make a family have eight sets of three children and then calculate which ones came out with two boys that just be crazy to be like on the kids oh my gosh I'm wondering about that 24 kids so eight eight ways we can accomplish our event out of eight possible outcomes remember these are called these things each individual one are called what what are these now these are probabilities Pugliese what we're calculating here this is our sample space the sample space is made up of every individual what type of event this is an event that's our main event made of end of the engine boat is right here and then we have mini events called sorts of s rhymes with ipil ipil i'm snipping my Apple there's simple events there they're an individual outcome so we need to get this down folks you know what a procedure is what's going on an event what your ultimate ly looking for simple events how your procedure can be accomplished and the way we find our probabilities take the things that accomplish our event divided by the total number of simple events that's what we have written and now give us a probability sound spaces this everything we could happen the sample space is made up of simple events quizzes so 37.5% so you know right now if boys and girls have an equal chance of occurring which they paid them it's really close so this is going to be very accurate for us if you ever go out there right now and have three kids don't do that without thinking about it you're going to go there have three kids you're going to have a 37.5% chance of having two boys and one girl you also have a 37.5 chance for some chance of getting two girls and one boy because there's three more of those probabilities can you find the probability of getting all three boys what's that one out of one at eight or all four-year-olds one and eight thankfully that that's a lower chance than two boys and one girl or two girls in one boy okay couple of milks for us before we go any further first even just a sense for you probabilities always have to be between zero and one you can't ever have a probability less than zero a negative chance of something happening what's the probability the rule of three negative to make sense all right so probabilities are between zero and one notes every probability calculated before we change it to a percentage was between zero and one can't be over one can't have more than a hundred said chance of something happening I know we kind of use that loosely in real life you go how much attention are you focusing on focused 110 percent or just a liar I think you focus hundred ten percent mathematically only you focus on our sentence makes sense yeah it's between zero one though so probabilities are always between zero and one and you can be zero what would a probability of zero be what does that imply about your event if you have a possibility of zero that would say that your event is impossible it's it'd be like this roll a die for me one time what's the probability of rolling a die and getting a rabbit go that's not that's not gonna happen right I'm not a magician but you just I am a musician I'm not a magician can't just make a rabbit appear from a dice I doesn't make sense so something that cannot happen is an impossible event with a probability with that in mind what's the probability equal to one imply we're done well this is possible that's not equal to one that's certainly possible right you can get two girls and a boy I say two boys and a girl you can get that so probability of one means it's more than possible it's certainly more than impossible Oda probability of one means more than just possible what's it mean it will happen it's certain it's certain if I say there's a hundred percent probability that you're going to have homework tonight that sucks huh that means that it's certain you were going to have homework tonight five percent probability P equals one means a certain event if you like this roll a die what's the probability in one two three four five or six you were going to give one of those numbers is certain also one other thing it's called the law of large numbers if you want to write down law of large numbers fill for this is what this makes I want you to think on this number flipping the coin well actually she's a contender flip the coin if we if you took a coin out and you flipped it ten times are you for sure going to get let's say it's a weight a nice even leeway to die so the probability of getting heads and tails is fifty-fifty if you flip it ten times are you for sure going to get five heads and five tails it's possible you get only three heads and seven tails right that's that's quite possible if you flip it a million times you're probably not going to get exactly 500,000 ads in five hundred thousand taels you're probably not going to going to get that but as you increase the number the observed probability is going to get very close to the classical probability for instance if you flip it ten times you might not get five and five if you flip it a million times it's going to be pretty close to 5050 you might get five four hundred and ninety thousand and five hundred ten thousand that ratio if you increase it to infinity observe probability will actually approach which means it's going to become classical probability so those two things will increase does that make sense to you the more you repeat a procedure the closer observed will be to classical theory you can see this in a poll under the polling that we did like the Dozen survey if you go out there to start only five people are they going to be very representative of the population of the United States of America it increases to a thousand is it more representative the increase of two three hundred million is it more representative that's like almost everybody you're like three hundred seven million people here so as you keep increasing your observed probability your observed results it's going to approach classical probability so that's a lot of large numbers as you increase our sorry the more procedures repeated the closer observed will be to classical publishing so the more procedures repeated the closer observe bundling we'll get to classical probability just swallowed large numbers more you do something the more your observations will mimic the theory or the more that what does happen will look like what should happen let me let me show what we talked about today it's any questions on pollinated stuff the law of large numbers or why probabilities are between 0 & 1 or why probably the 0 is impossible or 1 is it's definite that's going to happen or the difference between subjective classical or observed Pugliese you have any questions on those things or those ring a bell in your head does it make sense for you so when we say complimentary events what we're talking about in this class our events which are mutually exclusive have you ever heard that that phrase mutually exclusive you're heard of it number is this idea like it's a quickly mutually exclusive words are hard it says if you're in one group you're automatically discounted for being in another group you can't be in both at the same time have to be either here or you have to be here unless you really unless you're a strange dressing person you're either going to wear shoes or you're going to wear sandals right you're not going to wear both shoes and sandals at the same time I hope because that would just look ridiculous unless you deal with those kind of Teva look at things are kind of sandals - sandals chef would it be shadows at sandals shoes whatever anyway so you're not going to wear both the shoes and sandals at the same time right you're either wearing shoes or you're in sandals those groups or generally mutually exclusive so that's what that term means it means that you're either in one group or another there's no crossover basically so when we talk about complementary events but complementary events are our two events which are mutually exclusive I'll give you some better examples that relate to this classrooms a second by the way when you say complimentary I didn't spell it wrong it's not with the hi it's not like complement like you look nice today so these events are not saying they're going you're such a good looking event oh thank you event I feel like a good looking event today so I appreciate that compliment it's not that type of compliment it's it's this is the definition of their mutually exclusive one doesn't happen while the other one happens so they cannot happen the same time so complementary events these are events which are you to you Julie X will have a hard time I mutually I have sighs promise it's mutually I can't say that word just not today mutually exclusive the most basic definition I can give you from you to exclusive is to events which can't happen at the same time let's talk about just a basic example that okay let's bring back our dice the six-sided your substandard standard I okay I'd say okay I want you to roll the die can you get both a two and a five when your mother died once one time can you get both a two out of five those would be mutually exclusive events one of it would be willing to to the other that would be rolling five they've obviously cannot have at the same time when you're willing to die one time that would be mutually exclusive okay same thing like drawing out some cards drawing out the heart and drawn out me diamond if those are your events would be mutually exclusive events they won't happen the same time remember we talked about one event one procedure at a time not like draw three cards you can you get both the heart and a done yet you could in that case but for one card those would be mutually exclusive others you can finish in that they concept okay so what is a compliment for some notation if we have some event so let's say we have event paid the compliment of event a couplet of n a is denoted it looks a whole lot like me it's not but that's how we write the compliment you shall say this if we're talking about the compliment the compliment of something is a complement of an event is all the outcomes that occur that don't accomplish your event I'll repeat that for you so if we have a vente over here and we want to talk about the complement this is called the complement of a what this says is this is all the outcomes which don't satisfy this event does that make sense to you it's pretty much everything else that's what the complement is so the complement of event a is is denoted complement of a and is all the outcomes when a when event a does not occur does not occur for some reason this helps me to remember I don't know why the assessment memory but maybe this will help you remember it when you see this it's kind of like a minus sign - to me means not or bad not so if this is our event a this means not a so everything else besides a all the outcomes that don't make de you with me on that that's how I remember it don't know if that helps you hopefully that does so let's do an example let's say that my event let's go back to the the dice rolling thing okay the event is we're going to look to see if we can roll five so rolling a 5 that's orbit so if we call this event a so battles are a the complement would be a route that line on top of it or the complement of it what is the complement of rolling a 5 on a diet what do you think compliment of rolling a 5 what else couldn't happen to my answers question what else could happen you will die that doesn't make a 5 what else could you get basically could you get a 7 that's one time did you say what else could you get insights of 5 so anything besides the 5 in combat y'all stated 1 2 3 4 6 perfect so the complement of going to 5 is not going 5 or rolling not 5 for instance when yo people y'all stated here 1 2 3 4 & 6 that's a compliment so the compliment the complimentary events here work so that they add together to create the whole sample space so if you're talking about two complementary events it's got to be either one or the other the mutually exclusive but together they make it the whole thing can you get anything else besides a 5 or a 1 through 6 at some other complementary because together they make up the whole sample space right you can't get a 0 you can't get a 7 or anything else this is everything it could possibly happen they're just in two groups complementary events you have the five you have everything else that's the compliment of going to five we understand the compliment feel okay about that so far good now let's talk about the probability of these things so what's the probability let's say when I say five I'm a rolling a 5 ok what's the probability of rolling in 5 how many outcomes are going to let us accomplish our event of rolling a 5 how many outcomes let us roll with 5 how many files are on the die so there's only one specific outcome using a lot accomplished this particular event how many choices do we have so our probability is going to be one out of six you have millions can you tell me let's think about this if you have two events which are complimentary which means you're either in one event or the other and that takes care of everything that could possibly happen through what does the probability what is the probability of the complement of five or not rolling five have to be without even looking at how many choices you can people to figure this out can't we because you're either going to be here or you're going to be here so once you tell me if this is one six what does this one have to be for sure great how much do you think that a new probability of an event plus the probability of the complement of that event has to add up to all the time we think what is it going to add to the sum sure what's that some have to be he think was one yes you add those probabilities should you get one which stands for a 100% of everything right because you're either here either here or here you're not you're not anywhere else so if you add those probabilities together of the event plus the complement that accounts for everything that could possibly happen so there's your 100% certainly going to be in one of those two places does this make sense to you so probability of not going to five and you can see it I mean there's one two three there's five choices that you could have for not only two five or six possible choices we get five six seven five and we'll write that little note the probability of an event plus the probability of the complement of that event it has to equal warn all the time the probability of an event plus the probability of the complement must equal work it more basic terminology if you have a probability of some event plus the probability of its complement but you got one you we're going to kind of revisit this towards the Latin the latter part of section 4.3 this isn't kind of going to come back at you but if you understand it now that you're headed game do you understand why this takes place here if their view too exclusive you have to be either here here you can't be anywhere else so you add those probabilities together that accounts for everything you have a 1% probability that you're going to be in that net range do you guys feel good about the section 4.2 that we've talked about so far fill right with that again fun yet just lines I guess is it awesome so glad I'm here on Wednesday aren't you well let's see see our four point two we're going to go ahead and start four point three now

Channel: Professor Leonard

Views: 560,158

Keywords: Professor, Leonard, Statistics (Field Of Study), Probability (Measurement System), Lecture (Type Of Public Presentation), Math

Id: _EpXHuPnaK0

Length: 102min 11sec (6131 seconds)

Published: Sat Dec 10 2011