Intro to probability 1: Basic notation

hey guys what's up missed a nice here also known as AP stats guy and we're going to do some probability today basic probability we're probably going to do some probability as a matter of fact when people say probably they're actually are talking about probability chances likelihood so what the heck is probability produce a few examples so we can learn about the notation of probability okay so let's talk about some basic suppose I had a little satchel like this and inside I had some chips some poker chips colored red blue and green I had 10 chips in the bag let me just straight this camera will look a little bit off here there we go and I have these ten ships in a bag alright and I was wondering hey if I reach in randomly I pull out a chip what's the likelihood the chip has these qualities okay so let's see what we got we have five red to blue and three green ten chips all together so if I want to know hey what's the probability that I have I pull out a red chip I have to ask what are all the possibilities what could I pull out well let's see since there are ten ships and all out of the ten I could possibly grab in five red chips the probability that I pull out a red which we write like this probability that I pull out a red is five out of ten 50% is a 50% chance that I pull out a red well cool what's the probability a plot agree okay so let's put that let's put that red back in shake this up so all 10 her in here now let's see hmm what's the probability I pull out a green well how many greens are there let's say there's only three greens three greens out of ten and all would be three out of ten now we show probabilities sometimes like this we'll show it as five out of ten as a fraction but you can just do the calculation hmm 3/10 is point three and if you don't like doing that in your head you could do the your calculator 3/10 and it'll give you the same thing Oh point three which is 30% 5/10 is you know half of them is 50% chance so the public is read it's 50% the part of its green 30% but what if I want to know what's the probability it's red or green hmm red or green that would look like this what's the probability it's red or green rug now that doesn't say rug we have some symbols that we use in probability and here they are right above hovering above my head if you look up at them you have or is a you okay or then upside down it all kind of looks like an A and and it's like an upside down you okay you that's actually stands for Union so we get or and in given we're going to talk about those symbols or and and given but let's take a look at what's the probably is or green let's see red or green well how many ways can I get a red or a green um well if I pull out a red that would work or if I pull out a green because I need to do is pull out a red or a green and I have a success so if I pull out this okay okay okay yeah yeah not that one okay seems like this eight that are red or green out of 10 there's an 80% chance that I pick out a red or a green so that's a symbol for now what if what if I was wondering what's in likelihood I pull out one that's red and green huh red and green hmm what would that look like red and green what's the probability that I pull out red and green are there any that are red and green I didn't think so the likelihood up putting on a red and a green zero because there are none none of the he's none of these chips are red and green so he called because it can't be red or green at the same time they are mutually exclusive meaning they can't happen at the same time fancy word mutually exclusive mutually exclusive the other word we use for mutually exclusive two things that both can't happen at the same time disjoint because they're never going to be up in this joint at the same time know what I'm saying yeah now these are mutually exclusive events so things that can't happen at the same time we call mutually exclusive but some things can happen at the same time like suppose I said hmm what's the probability that a random well let's see red me and ABI what's the probability I randomly pull one out what does this say II what could that stand for even what's it likelihood a random ship is even well let's see I agree Jim whoo how many even chips are there 2 4 6 8 10 there are 5 even chips out of the 10 like evidence even is 0.5 or 50% chance hmm what's the probability it's even and red oh my god even and red which ones of these are both even and right now we have this thing and and in order to follow to be have some and quality both things have to be true so it has to be both even and red let's take a look is this even an red and even in red yeah even in red uh even if it's me no no no I'll be even I mean we're gonna happy this guy's on me you're not red I mean you're green man you're not red in order to fall into this category you have to be even and red and there's only two out of the ten that are even and red both qualities have to be true so we have this thing or either/or it's okay and both have to be true let's look at another or for the heck of it why I don't know what's the probability that it's green or odd green or odd hmm so basically I'm saying hey you win a prize if you pull out a green or an odd so as long as you have at least one of these qualities green or odd you win so let's see who wins so you reach in the bag you're like I want to win you want a million dollars if it's green or odd you reach it if you pull out a green you're gonna be like I won if you pull out or not even like I win so let's see you put a 1 ah very nice you win what about a 2 and neither green nor odd 3 odd for now neither green nor 5 odd math sevens odd H not odd but it's green and I told you when it was green or odd yeah 9 is both so you're also when you don't win double ok just win a million bucks as long as one of the other so green or odd how many fall into that how many winners are there if it's green or odd it's green ah or both reading odd 1 2 3 4 5 6 7 Wow 7 out of 10 there's a 70% chance you win the money if it's green or odd hmm or so that's or or Union now the last symbol the last symbol whence like luck is this one it's given and I think of it it's like a it's like a slice and it's slicing up the pie notice that all these other ones that we did the denominator was 10 because inside this bucket inside this bag all 10 chips are in the bag for every one of those the ands the ORS the individual ones now we're gonna slice up the bag we're gonna change what's in the bag ha ha change what's inside the bag so the denominator changes and it's called given given I'm going to give you some information so it looks like this ooh are any up there look at that mean red even and what this says is the following what is the probability that it's red given the information that it's even so what this means is I reach in I'm telling you something it's even now what's the likelihood that it's red so what you have to imagine is the only things I can choose from I'm telling you it's even so just pretend the bag only has evens in it so how many are in the bag and all the given information is the new denominator how many evens are there and all well let's take a look hmm let's see the evens that would be near the to the for the sixth the eight the ten there would be five things in here I'm telling you it's even now out of those five now what's the likelihood it's red now you know it's even let's see which of those evens are red out of those one two three four five evens two out of the five I read so you know what that means the likelihood that it's red given the information that it's even is 2/5 which is also if I put in my calculator 40% chance isn't that the same thing if I said what's the probability it's even give it it's red let's see hmm it's probably it's even giving it's red hmm it's red what's in the bag now let's change it what's a bird ability is even given its read now think of what's going on now I'm telling you some information the only thing that's in the bag are these guys there's only red chips in the bag I'm telling you hey these are all red now what's the likelihood that it's even let's see how many Reds are there let's see which ones are red red red red like a roosters head there's 5 Reds even 2 out of 5 good that's 40% so whether it's e r or r e it must be the same thing no watch see if we can find us one what's the probability that is even given it's green how many greens at all what's in the bag only greens how many are even of these greens hominy or even mm-hmm so remember Paul the bag had and it was greens two out of the three now let's switch it around the other way what's the probability was Green given it was even well isn't that gonna be the same thing I don't know think about it I'm telling you what's in the bag just even yeah I dropped the bag up how many evens are in there 5 2 4 6 8 and 10 so let's see here's my evens 2 4 6 8 10 how many of those are green out of those five june-june two out of five uh-huh not always the same thing did you fall for my trick mmm now here we go check it out basic stuff okay basic symbols you're going to see one looks like this that means or if this or that or both you're out of the party if I was like hey man stand up viewer in jeans or a woman you'd stand up if you're wearing jeans or if you're a woman or if you're a woman wearing jeans or and looks like this both qualities have to be true looks like an A and this this and this have to both be happening at the same time and the last symbol that we use an awful lot my favorite yeah I'm just chopping up I'm changing what's in about giving you the information giving you information what's in the bag is changing so it's not everything the denominators changing when you see this so who's in the bag like one more example because you have a lot of issues with this so if I said what's the probability it is blue give it it too even what's going to be in the bag just even so this just evens in the bag how many evens are there 5 of those 5 evens or by evens 2 4 6 8 and 10 of my evens of those 5 evens which ones are blue just one what's private is blue given it's even 20% so that's the basic the basic symbology don't forget or and give it hopefully that makes a little bit of sense to begin with we can do some more videos and a little bit we're going to talk about independence I'm going to talk about the general multiplication rule the general addition rule and all kinds of other weird rules but they're kind of like common sense rules if you think about it so we're going on have a great day I hope you're loving stats

Channel: MrNystrom

Views: 92,498

Rating: 4.9418669 out of 5

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Id: TkU3BvDAOtQ

Length: 14min 37sec (877 seconds)

Published: Tue Dec 29 2015