Intro to probability 2: Independent and disjoint (

what's up here it's AI AP stats guy I'm coming at you with a little bit more probability stuff we're going to talk about independence and disjoint something that we always get mixed up but if we can separate those two ideas in our mind it'll all start making sense so the first thing I'm going to talk about is independence and what it is and then we'll look at this joint events and see that they can't be independent it's impossible stay with me so we get up here if those of you guys the first video you saw it when I imagine having a bag a little satchel filled with poker chips and the poker chips are colored red blue and green and they're also numbered so they're colored in their number okay those are two different qualities the variables I guess the random variables your color and number okay so they're numbered and colored and we're going to look at a couple of different events we're going to think things happening so we look at the its status of its color status and its number status so we're going to look at blue and even so overall we talked about basic probability here so what's the probability of random chip if I reach in what's it likely that I pull out a blue well out of the ten chips how many are blue well this two out of ten so it gives me the likelihood of 20% point two now let's look at even like is that a random chip is even well if I reach in mmm okay this 10 chips and all how many of those chips are even let's see out of the ten chips two four six eight ten five or even there's a 50% chance it's even now here's my question though what's the probability it's blue if I first tell you that it's even now that's something called a given it's a conditional I'm giving you a condition I'm saying hey I'm going to tell you it's even now you know it's even knowing it's even did it change the likelihood of it being blue let's see well what's in the bag now hey yeah that bomb I'm changing what's in the bag what's the probability it's blue given the information that it's even so I'm telling you what's in the bag here just evens out of those evens which ones are blue let's see here by even two two two two two two four six eight ten out of those five notice I changed the denominator goes five how many of them are blue one one out of five point two so look at that the likelihood of it being blue is 20% chance if I tell you it's even the likelihood of it being blue is 20% chance that's what independence is me telling you hey it's even did not change the likelihood of it being blue either way it's still a 20% chance being blue blue status and being even are independent and you can see but the probability of blue is the same knowing it's even and that's where the check like the equation you can check independent events when you know that the probability and the generically they use a and B we had B and E but we just found out the probability of blue is the same even when you tell me it's evil probability a blue is still the probability of blue and I know what's even so we say blue and even on independent the generic way to look at is the probability of a equals a part of a when you're given B we say a and B are independent now we say blue and even status blue status because that's our independent cool something else cool happened though we have the probability of blue is 0.2 probably being even we saw was five out of ten which was what POY sorry 50% what about the likelihood of being blue and even at the same time how many of them at all are blue and even well out of all of these how many are in the bag now notice there's no slash so we still have ten in the bag what's it likely that I pull out one that's blue and even uh-huh well how many blue and evens are there let's see and just one that's blue and even one out of 10 which is 0.1 an interesting observation notice hmmm-hmmm-hmmm point two times 0.5 equals 0.1 this is another way you can check for independence if the probability of one times are probably the other equals the probability than both happening at the same time which happens here it's another check for independence take a look probability of B times the probability of E in this case does equal the probability of B and E 0.2 times 0.5 does equal point one that's another check for independence so there's two ways to check okay two equations but basically what independence means independence means telling you this information does not change the likelihood of the other for instance if I reach ticket deck of cards and I say Who what's the likelihood that it's a red card and you say 50 percent chance what if I first tell you it's a king still a 50 percent chance because 50 percent of the Kings are red also so being a king and being red are independent okay that's what independence is so here are the two equations if the probability of a doesn't change knowing B is true we say that they're independent B does not impact AIDS likelihood of occurring the other thing we know to check for independence if the likelihood of a probability of a times probability B is the likelihood of them happening at the same time sorry what doesn't matter the order a and B those are the two equations to check for independence now then what happens if they're not independent well let's look at two things that are not independent green and even let's look at green and even let's see I have a feeling because they're not independent these won't be equal nor will these well let's find out let's check green the probability of reading the probability even and the probability of green and even and probability of green giving over all the probability of green let's see how many greens there are in this bag there are ten only three are green three out of ten which is a 30% chance of getting a green the likelihood of getting it even we saw that four is five out of ten it's a 50% chance what's the likelihood it's green and even well I reach in the bag remember I didn't change what's in the bag there's still 10 in the bag the only time I change what's in the bag I I chop it up and take a little bit out of the bag what's the likelihood it's green and even well out of all ten how many are green and even two out of the ten are green and even what's the probability of green given it's even now I'm telling you all that's in the bag the only thing that's in the bag now are evens oh look at all those evens how many evens are in my bag there are only five evens of the five evens here my five even even even even even even how many of those are two out of the five which is point four let's check for independence green and even if they are independent and shouldn't the probability of green be the same when I know that it's even let's see if this is true if this is true they're independent well the probability of being green is point three is it the same does it change knowing it's even it goes up to 0.4 knowing it's even increase the likelihood of it being green okay so we say since those are not equal they're not independent cool which means we say they're associated let's check the other equation we know well it green and even were independent we know that the probability of green times the probability of even would equal the probability of green and even well the probability of green is 0.3 the probability of even is 0.5 0.3 point five the pivot of green and even green and even is point two is point three five point five equal to point two know what point 1 5 is not equal to 0.2 not independent so knowing even changes the likelihood of being green and just like knowing green would change the likelihood of being even because they're associated think about it what's the likelihood that one of these is randomly even you know a 1/2 chance but what if I tell you it's green are half of the greens even know two out of the three I've knowing it's green increase the likelihood of it being even so they're not independent how does this joint play into this well disjoint and talked about it before we'll talk about it again disjoint are two things that I'm going to be up in this joint together disjoint is the same thing as mutually exclusive they can't happen at the same time and because they can't happen at the same time they can't be independent stop and think about that for a second let's look at disjoint being green and being blue none of the chips are blue and green are they so let's look at the probability of being blue let's look at the probability of being green well the probability in blue overall is two out of ten which is a 20% chance the problems being green overall is 3 out of 10 which is a 30% chance now let's look at the other probabilities what's the probability of blue if I tell you it's green and what's the probability of being blue and green at the same time ready I read you to the bag I pull out I tell you something about the chip I'm giving you this information this is a condition here's the condition conditional I'm telling you this chip is green now what's the likelihood it's blue zero now now what's a lucky hood of chip is blue and green zero they can't be blue and green a chip only has one individual color so it should make sense if you think about what the equations say did the likelihood of being blue change when you knew green yes it change it changed significantly it won from a 20% chance to a 0% chance remember what the equation says to check for independence things are independent this is how it looks generically if the probability of a is the same when you know B is true then they're independent so my question is saying to you with blue and green is the likelihood of blue the same when I tell you that it's green no because the probably being blue overall is 20% but if I tell you it's green it changes to zero knowing it's green change its likelihood to zero so there we go since those are people they can't be independent using the other equation does the probability of blue times the probability of green equal the probability of blue and green well the probability of blue is point to the primitive Green is 0.3 there's 0.2 times 0.3 equal zero because they can't have no so if they're disjoint they can't be independent the reason why they can't be independent because when they're disjoint if you know one thing is true the likelihood of the other becomes zero okay independent means if you know one is true it doesn't impact the likelihood of the other here we saw overall was 20% chance it to be blue but if I knew was green that chance went to zero so independent jump events do not impact the likelihood of each other happening okay being even and being blue knowing it's even doesn't change the likelihood of it being blue knowing it's blue it doesn't change the likelihood of it being even green and blue whoa disjoint that totally changed so that's a dip sweet independence and disjoint I hope that helped you good luck go get them episodes

Channel: MrNystrom

Views: 69,281

Rating: 4.9260354 out of 5

Keywords: Disjoint independent mutually exclusive ap stats statistics Mr nystrom

Id: GnWHt9nqwBA

Length: 12min 54sec (774 seconds)

Published: Wed Dec 30 2015