Sentence stringlengths 101 2.5k | video_title stringlengths 44 104 |
|---|---|
But it could get very complicated if I said, hey, I have 100 seats and I have 100 people that are going to sit in them. How do I figure it out mathematically? Well, the way that you would do it, and this is going to be a technique that you can use for really any number of people in any number of seats, is to really jus... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
What we did here is we started with seat number one. And we said, all right, how many different possibilities are, how many different people could sit in seat number one, assuming no one has sat down before? Well, three different people could sit in seat number one. You can see it right over here. This is where A is si... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
You can see it right over here. This is where A is sitting in seat number one. This is where B is sitting in seat number one. And this is where C is sitting in seat number one. Now for each of those three possibilities, how many people can sit in seat number two? Well, we saw when A sits in seat number one, there's two... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
And this is where C is sitting in seat number one. Now for each of those three possibilities, how many people can sit in seat number two? Well, we saw when A sits in seat number one, there's two different possibilities for seat number two. When B sits in seat number one, there's two different possibilities for seat num... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
When B sits in seat number one, there's two different possibilities for seat number two. When C sits in seat number one, this is a tongue twister, there's two different possibilities for seat number two. And so you're gonna have two different possibilities here. Another way to think about it is, one person has already ... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
Another way to think about it is, one person has already sat down here, there's three different ways to getting that, and so there's two people left who could sit in the second seat. And we saw that right over here where we really wrote out the permutations. And so how many different permutations are there for seat num... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
Well, you would multiply. For each of these three, you have two, for each of these three in seat number one, you have two in seat number two. And then what about seat number three? Well, if you know who's in seat number one and seat number two, there's only one person who can be in seat number three. And another way to... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
Well, if you know who's in seat number one and seat number two, there's only one person who can be in seat number three. And another way to think about it, if two people have already sat down, there's only one person who could be in seat number three. And so mathematically, what we could do is just say three times two ... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
And you might recognize the mathematical operation factorial which literally just means, hey, start with that number and then keep multiplying it by the numbers one less than that and then one less than that all the way until you get to one. And this is three factorial which is going to be equal to six which is exactly... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
Let's say that we have five seats, one, two, three, four, five, and we have five people, person A, B, C, D, and E. How many different ways can these five people sit in these five seats? Pause this video and figure it out. Well, you might immediately say, well, that's going to be five factorial which is going to be equa... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
Five times four is 20. 20 times three is 60. And then 60 times two is 120. And then 120 times one is equal to 120. And once again, that makes a lot of sense. There's five different, if no one sat down, there's five different possibilities for seat number one. And then for each of those possibilities, there's four peopl... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
And then 120 times one is equal to 120. And once again, that makes a lot of sense. There's five different, if no one sat down, there's five different possibilities for seat number one. And then for each of those possibilities, there's four people who could sit in seat number two. And then for each of those 20 possibili... | Factorial and counting seat arrangements Probability and Statistics Khan Academy.mp3 |
So given that definition of a random variable, what we're going to try to do in this video is think about the probability distribution. So what's the probability of the different possible outcomes or the different possible values for this random variable? And we'll plot them to see how that distribution is spread out a... | Constructing a probability distribution for random variable Khan Academy.mp3 |
So let's think about all of the different values that you could get when you flip a fair coin three times. So you could get all heads. Heads, heads, heads. You could get heads, heads, tails. You could get heads, tails, heads. You could get heads, tails, tails. You could have tails, heads, head. | Constructing a probability distribution for random variable Khan Academy.mp3 |
You could get heads, heads, tails. You could get heads, tails, heads. You could get heads, tails, tails. You could have tails, heads, head. You could have tails, head, tails. You could have tails, tails, heads. And then you could have all tails. | Constructing a probability distribution for random variable Khan Academy.mp3 |
You could have tails, heads, head. You could have tails, head, tails. You could have tails, tails, heads. And then you could have all tails. So when you do the actual experiment, there's eight equally likely outcomes here. But which of them, how would these relate to the value of this random variable? So let's think ab... | Constructing a probability distribution for random variable Khan Academy.mp3 |
And then you could have all tails. So when you do the actual experiment, there's eight equally likely outcomes here. But which of them, how would these relate to the value of this random variable? So let's think about what's the probability. There is a situation where you have zero heads. So we could say, what's the pr... | Constructing a probability distribution for random variable Khan Academy.mp3 |
So let's think about what's the probability. There is a situation where you have zero heads. So we could say, what's the probability that our random variable X is equal to 0? Well, that's this situation right over here where you have zero heads. It is one out of the eight equally likely outcomes. So that's going to be ... | Constructing a probability distribution for random variable Khan Academy.mp3 |
Well, that's this situation right over here where you have zero heads. It is one out of the eight equally likely outcomes. So that's going to be 1 over 8. What's the probability that our random variable capital X is equal to 1? Well, let's see. Which of these outcomes gets us exactly one head? We have this one right ov... | Constructing a probability distribution for random variable Khan Academy.mp3 |
What's the probability that our random variable capital X is equal to 1? Well, let's see. Which of these outcomes gets us exactly one head? We have this one right over here. We have that one right over there. We have this one right over there. And I think that's all of them. | Constructing a probability distribution for random variable Khan Academy.mp3 |
We have this one right over here. We have that one right over there. We have this one right over there. And I think that's all of them. So three out of the eight equally likely outcomes get us to one head, which is the same thing as saying that our random variable equals 1. So this has a 3 8's probability. Now, what's ... | Constructing a probability distribution for random variable Khan Academy.mp3 |
And I think that's all of them. So three out of the eight equally likely outcomes get us to one head, which is the same thing as saying that our random variable equals 1. So this has a 3 8's probability. Now, what's the probability? I think you're maybe getting the hang for it at this point. What's the probability that... | Constructing a probability distribution for random variable Khan Academy.mp3 |
Now, what's the probability? I think you're maybe getting the hang for it at this point. What's the probability that our random variable X is going to be equal to 2? Well, for X to be equal to 2, that means we got two heads when we flipped the coin three times. So this outcome meets that constraint. This outcome would ... | Constructing a probability distribution for random variable Khan Academy.mp3 |
Well, for X to be equal to 2, that means we got two heads when we flipped the coin three times. So this outcome meets that constraint. This outcome would get our random variable to be equal to 2. And this outcome would make our random variable equal to 2. And this is three out of the eight equally likely outcomes. So t... | Constructing a probability distribution for random variable Khan Academy.mp3 |
And this outcome would make our random variable equal to 2. And this is three out of the eight equally likely outcomes. So this has a 3 8's probability. And then finally, we could say, what is the probability that our random variable X is equal to 3? Well, how does our random variable X equal 3? Well, we would have to ... | Constructing a probability distribution for random variable Khan Academy.mp3 |
And then finally, we could say, what is the probability that our random variable X is equal to 3? Well, how does our random variable X equal 3? Well, we would have to get three heads when we flip the coin. So there's only one out of the eight equally likely outcomes that meets that constraint. So it's a 1 8 probability... | Constructing a probability distribution for random variable Khan Academy.mp3 |
So there's only one out of the eight equally likely outcomes that meets that constraint. So it's a 1 8 probability. So now we just have to think about how we plot this to really see how it's distributed. So let me draw over here on the vertical axis. I'll draw this will be the probability. And it's going to be between ... | Constructing a probability distribution for random variable Khan Academy.mp3 |
So let me draw over here on the vertical axis. I'll draw this will be the probability. And it's going to be between 0 and 1. You can have a probability larger than 1. So just like this. So let's see. If this is 1 right over here. | Constructing a probability distribution for random variable Khan Academy.mp3 |
You can have a probability larger than 1. So just like this. So let's see. If this is 1 right over here. And let's see. Everything here, it looks like it's an eighth. So let's put everything in terms of eighths. | Constructing a probability distribution for random variable Khan Academy.mp3 |
If this is 1 right over here. And let's see. Everything here, it looks like it's an eighth. So let's put everything in terms of eighths. So that's half. This is a fourth. That's a fourth. | Constructing a probability distribution for random variable Khan Academy.mp3 |
So let's put everything in terms of eighths. So that's half. This is a fourth. That's a fourth. That's not quite a fourth. This is a fourth right over here. And then we can do it in terms of eighths. | Constructing a probability distribution for random variable Khan Academy.mp3 |
That's a fourth. That's not quite a fourth. This is a fourth right over here. And then we can do it in terms of eighths. So that's a pretty good rough approximation. And then over here, we could have the outcomes. And so outcomes, I'll say outcomes for, or let's write this so value. | Constructing a probability distribution for random variable Khan Academy.mp3 |
And then we can do it in terms of eighths. So that's a pretty good rough approximation. And then over here, we could have the outcomes. And so outcomes, I'll say outcomes for, or let's write this so value. So value for X. So X could be 0, 1. Actually, let me do those same colors. | Constructing a probability distribution for random variable Khan Academy.mp3 |
And so outcomes, I'll say outcomes for, or let's write this so value. So value for X. So X could be 0, 1. Actually, let me do those same colors. X could be 0. X could be 1. X could be 2. | Constructing a probability distribution for random variable Khan Academy.mp3 |
Actually, let me do those same colors. X could be 0. X could be 1. X could be 2. X could be equal to 2. And X could be equal to 3. These are the possible values for X. | Constructing a probability distribution for random variable Khan Academy.mp3 |
X could be 2. X could be equal to 2. And X could be equal to 3. These are the possible values for X. And now we're just going to plot the probability. The probability that X has a value of 0 is 1 eighth. So I'll make a little bar right over here that goes up to 1 eighth. | Constructing a probability distribution for random variable Khan Academy.mp3 |
These are the possible values for X. And now we're just going to plot the probability. The probability that X has a value of 0 is 1 eighth. So I'll make a little bar right over here that goes up to 1 eighth. So actually, let me draw it like this. So this is 1 eighth right over here. The probability that X equals 1 is 3... | Constructing a probability distribution for random variable Khan Academy.mp3 |
So I'll make a little bar right over here that goes up to 1 eighth. So actually, let me draw it like this. So this is 1 eighth right over here. The probability that X equals 1 is 3 eighths. So that's 2 eighths, 3 eighths. Gets us right over. Let me do that in that purple color. | Constructing a probability distribution for random variable Khan Academy.mp3 |
The probability that X equals 1 is 3 eighths. So that's 2 eighths, 3 eighths. Gets us right over. Let me do that in that purple color. So probability of 1, that's 3 eighths. That's right over there. That's 3 eighths. | Constructing a probability distribution for random variable Khan Academy.mp3 |
Let me do that in that purple color. So probability of 1, that's 3 eighths. That's right over there. That's 3 eighths. So let me draw that bar. Just like that. The probability that X equals 2 is also 3 eighths. | Constructing a probability distribution for random variable Khan Academy.mp3 |
That's 3 eighths. So let me draw that bar. Just like that. The probability that X equals 2 is also 3 eighths. So that's going to be that same level, just like that. And then the probability that X equals 3, well, that's 1 eighth. So it's going to be the same height as this thing right over here. | Constructing a probability distribution for random variable Khan Academy.mp3 |
The probability that X equals 2 is also 3 eighths. So that's going to be that same level, just like that. And then the probability that X equals 3, well, that's 1 eighth. So it's going to be the same height as this thing right over here. So actually, I'm using the wrong color. So it's going to look like this. It's goin... | Constructing a probability distribution for random variable Khan Academy.mp3 |
So it's going to be the same height as this thing right over here. So actually, I'm using the wrong color. So it's going to look like this. It's going to look like this. And actually, let me just write this a little bit neater. I can move that 3. So cut and paste. | Constructing a probability distribution for random variable Khan Academy.mp3 |
It's going to look like this. And actually, let me just write this a little bit neater. I can move that 3. So cut and paste. Let me move that 3 a little bit closer in, just so it looks a little bit neater. And I can move that 2 in, actually, as well. So cut and paste. | Constructing a probability distribution for random variable Khan Academy.mp3 |
So cut and paste. Let me move that 3 a little bit closer in, just so it looks a little bit neater. And I can move that 2 in, actually, as well. So cut and paste. So I can move that 2. And there you have it. We have made a probability distribution for the random variable X. | Constructing a probability distribution for random variable Khan Academy.mp3 |
So cut and paste. So I can move that 2. And there you have it. We have made a probability distribution for the random variable X. And the random variable X can only take on these discrete values. It can't take on the value half or the value pi or anything like that. And so what we've just done here is we've just constr... | Constructing a probability distribution for random variable Khan Academy.mp3 |
We have made a probability distribution for the random variable X. And the random variable X can only take on these discrete values. It can't take on the value half or the value pi or anything like that. And so what we've just done here is we've just constructed a discrete probability distribution. Let me write that do... | Constructing a probability distribution for random variable Khan Academy.mp3 |
Let's do a little bit of probability with playing cards. And for the sake of this video, we're going to assume that our deck has no jokers in it. You could do the same problems with the joker. You'll just get slightly different numbers. So with that out of the way, let's first just think about how many cards we have in... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
You'll just get slightly different numbers. So with that out of the way, let's first just think about how many cards we have in a standard playing deck. So you have four suits. So you have four suits. And the suits are the spades, the diamonds, the clubs, and the hearts. You have four suits. And then in each of those s... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So you have four suits. And the suits are the spades, the diamonds, the clubs, and the hearts. You have four suits. And then in each of those suits, you have 13 different types of cards. Or sometimes it's called the rank. So each suit has 13 types of cards. You have the ace, then you have the two, the three, the four, ... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
And then in each of those suits, you have 13 different types of cards. Or sometimes it's called the rank. So each suit has 13 types of cards. You have the ace, then you have the two, the three, the four, the five, the six, seven, eight, nine, 10. And then you have the jack, the king, and the queen. And that is 13 cards... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
You have the ace, then you have the two, the three, the four, the five, the six, seven, eight, nine, 10. And then you have the jack, the king, and the queen. And that is 13 cards. So for each suit, you can have any of these. For any of these, you can have any of the suits. So you could have a jack of diamonds, a jack o... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So for each suit, you can have any of these. For any of these, you can have any of the suits. So you could have a jack of diamonds, a jack of clubs, a jack of spades, or a jack of hearts. So if you just multiply these two things, you could take a deck of playing cards and actually count them, take out the jokers and co... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So if you just multiply these two things, you could take a deck of playing cards and actually count them, take out the jokers and count them. But if you just multiply this, you have four suits. Each of those suits have 13 types. So you're going to have 4 times 13 cards. Or you're going to have 52 cards in a standard pl... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So you're going to have 4 times 13 cards. Or you're going to have 52 cards in a standard playing deck. Another way you could say it, you're like, look, I'm going to have these ranks or types. And each of those come in four different suits, 13 times 4. Once again, you would have gotten 52 cards. Now with that out of the... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
And each of those come in four different suits, 13 times 4. Once again, you would have gotten 52 cards. Now with that out of the way, let's think about the probabilities of different events. So let's say I shuffle that deck. I shuffle it really, really well. And then I randomly pick a card from that deck. And I want to... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So let's say I shuffle that deck. I shuffle it really, really well. And then I randomly pick a card from that deck. And I want to think about what is the probability that I pick a jack. Well, how many equally likely events are there? Well, I could pick any one of those 52 cards. So there's 52 possibilities for when I p... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
And I want to think about what is the probability that I pick a jack. Well, how many equally likely events are there? Well, I could pick any one of those 52 cards. So there's 52 possibilities for when I pick that card. And how many of those 52 possibilities are jacks? Well, you have the jack of spades, the jack of diam... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So there's 52 possibilities for when I pick that card. And how many of those 52 possibilities are jacks? Well, you have the jack of spades, the jack of diamonds, the jack of clubs, and the jack of hearts. There's four jacks in that deck. So it is 4 over 52. These are both divisible by 4. 4 divided by 4 is 1. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
There's four jacks in that deck. So it is 4 over 52. These are both divisible by 4. 4 divided by 4 is 1. 52 divided by 4 is 13. Now let's think about the probability. So we're going to start over. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
4 divided by 4 is 1. 52 divided by 4 is 13. Now let's think about the probability. So we're going to start over. I'm going to put that jack back in. I'm going to reshuffle the deck. So once again, I still have 52 cards. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So we're going to start over. I'm going to put that jack back in. I'm going to reshuffle the deck. So once again, I still have 52 cards. So what's the probability that I get a hearts? What's the probability that I just randomly pick a card from a shuffled deck and it is a hearts? Its suit is a heart. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So once again, I still have 52 cards. So what's the probability that I get a hearts? What's the probability that I just randomly pick a card from a shuffled deck and it is a hearts? Its suit is a heart. Well, once again, there's 52 possible cards I could pick from, 52 possible equally likely events that we're dealing w... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Its suit is a heart. Well, once again, there's 52 possible cards I could pick from, 52 possible equally likely events that we're dealing with. And how many of those have our hearts? Well, essentially 13 of them are hearts. For each of those suits, you have 13 types. So there are 13 hearts in that deck. There are 13 dia... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Well, essentially 13 of them are hearts. For each of those suits, you have 13 types. So there are 13 hearts in that deck. There are 13 diamonds in that deck. There are 13 spades in that deck. There are 13 clubs in that deck. So 13 of the 52 would result in hearts. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
There are 13 diamonds in that deck. There are 13 spades in that deck. There are 13 clubs in that deck. So 13 of the 52 would result in hearts. And both of these are divisible by 13. This is the same thing as 1 fourth. 1 and 4 times, I will pick it out or I have a 1 and 4 probability of getting a hearts when I go to tha... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So 13 of the 52 would result in hearts. And both of these are divisible by 13. This is the same thing as 1 fourth. 1 and 4 times, I will pick it out or I have a 1 and 4 probability of getting a hearts when I go to that, when I randomly pick a card from that shuffle deck. Now let's do something that's a little bit more ... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
1 and 4 times, I will pick it out or I have a 1 and 4 probability of getting a hearts when I go to that, when I randomly pick a card from that shuffle deck. Now let's do something that's a little bit more interesting. Or maybe it's a little obvious. What's the probability that I pick something that is a jack? I'll just... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
What's the probability that I pick something that is a jack? I'll just write J. It's a jack and it is a hearts. Well, if you're reasonably familiar with cards, you'll know that there's actually only one card that is both a jack and a heart. It is literally the jack of hearts. So we're saying, what is the probability th... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Well, if you're reasonably familiar with cards, you'll know that there's actually only one card that is both a jack and a heart. It is literally the jack of hearts. So we're saying, what is the probability that we pick the exact card, the jack of hearts? Well, there's only one event, one card, that meets this criteria ... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Well, there's only one event, one card, that meets this criteria right over here. And there's 52 possible cards. So there's a 1 in 52 chance that I pick the jack of hearts, something that is both a jack and it's a heart. Now let's do something a little bit more interesting. What is the probability? You might want to pa... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Now let's do something a little bit more interesting. What is the probability? You might want to pause this and think about this a little bit before I give you the answer. What is the probability of, so I once again, I have a deck of 52 cards. I shuffle it, randomly pick a card from that deck. What is the probability t... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
What is the probability of, so I once again, I have a deck of 52 cards. I shuffle it, randomly pick a card from that deck. What is the probability that that card that I pick from that deck is a jack or a heart? So it could be the jack of hearts or it could be the jack of diamonds or it could be the jack of spades or it... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So it could be the jack of hearts or it could be the jack of diamonds or it could be the jack of spades or it could be the queen of hearts or it could be the two of hearts. So what is the probability of this? And this is a little bit more of an interesting thing because we know, first of all, that there are 52 possibil... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
There are 52 possibilities. But how many of those possibilities meet the criteria, meet these conditions that it is a jack or a heart? And to understand that, I'll draw a Venn diagram. Sounds kind of fancy, but nothing fancy here. So imagine that this rectangle I'm drawing here represents all of the outcomes. So if you... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Sounds kind of fancy, but nothing fancy here. So imagine that this rectangle I'm drawing here represents all of the outcomes. So if you want, you can imagine it has an area of 52. So this is 52 possible outcomes. Now, how many of those outcomes result in a jack? So we already learned, it's one out of 13 of those outcom... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So this is 52 possible outcomes. Now, how many of those outcomes result in a jack? So we already learned, it's one out of 13 of those outcomes result in a jack. So I could draw a little circle here where that area, and I'm approximating, that represents the probability of a jack. So it should be roughly 1 13th or 4 52n... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So I could draw a little circle here where that area, and I'm approximating, that represents the probability of a jack. So it should be roughly 1 13th or 4 52nds of this area right over here. So I'll just draw it like this. So this right over here is the probability of a jack. The probability of the jack. It is four, t... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So this right over here is the probability of a jack. The probability of the jack. It is four, there's four possible cards out of the 52. So that is four 52nds or one out of 13. 1 13. Now, what's the probability of getting a hearts? Well, I'll draw another little circle here that represents that. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So that is four 52nds or one out of 13. 1 13. Now, what's the probability of getting a hearts? Well, I'll draw another little circle here that represents that. 13 out of 52. 13 out of these 52 cards represent a heart. And actually, one of them represents both a heart and a jack. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Well, I'll draw another little circle here that represents that. 13 out of 52. 13 out of these 52 cards represent a heart. And actually, one of them represents both a heart and a jack. So I'm actually going to overlap them, and hopefully this will make sense in a second. So there's actually 13 cards that are a heart. S... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
And actually, one of them represents both a heart and a jack. So I'm actually going to overlap them, and hopefully this will make sense in a second. So there's actually 13 cards that are a heart. So this is the number of hearts. Number of hearts. And actually, let me write this top thing that way as well. That makes it... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So this is the number of hearts. Number of hearts. And actually, let me write this top thing that way as well. That makes it a little bit clearer that we're actually looking at. So let me clear that. So the number of jacks. Number of jacks. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
That makes it a little bit clearer that we're actually looking at. So let me clear that. So the number of jacks. Number of jacks. And of course, this overlap right here is the number of jacks and hearts. The number of items out of this 52 that are both a jack and a heart. It is in both sets here. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Number of jacks. And of course, this overlap right here is the number of jacks and hearts. The number of items out of this 52 that are both a jack and a heart. It is in both sets here. It is in this green circle, and it is in this orange circle. So this right over here, let me do that in yellow since I did that problem... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
It is in both sets here. It is in this green circle, and it is in this orange circle. So this right over here, let me do that in yellow since I did that problem in yellow. This right over here is the number of jacks and hearts. So let me draw a little arrow there. It's getting a little cluttered. Maybe I should have dr... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
This right over here is the number of jacks and hearts. So let me draw a little arrow there. It's getting a little cluttered. Maybe I should have drawn a little bit bigger. Number of jacks and hearts. Number of jacks and hearts. And that's an overlap over there. | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Maybe I should have drawn a little bit bigger. Number of jacks and hearts. Number of jacks and hearts. And that's an overlap over there. So what is the probability of getting a jack or a heart? So if you think about it, the probability is going to be the number of events that meet these conditions over the total number... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
And that's an overlap over there. So what is the probability of getting a jack or a heart? So if you think about it, the probability is going to be the number of events that meet these conditions over the total number of events. We already know the total number of events are 52, but how many meet these conditions? So i... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
We already know the total number of events are 52, but how many meet these conditions? So it's going to be the number, it's going to be, you could say, well, look, the green circle right there says the number that gives us a jack, and the orange circle tells us that the number that gives us a heart. So you might want t... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
But if you did that, you would be double counting. Because if you added up, if you just did four, if you did four plus 13, what are we saying? We're saying that there are four jacks, and we're saying that there are 13 hearts. But in both of these, when we do it this way, in both cases, we are counting the jack of heart... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
But in both of these, when we do it this way, in both cases, we are counting the jack of hearts. We're putting the jack of hearts here, and we're putting the jack of hearts here. So we're counting the jack of hearts twice, even though there's only one card there. So you would have to subtract out where they're common. ... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So you would have to subtract out where they're common. You would have to subtract out the item that is both a jack and a heart. So you would subtract out a one. Another way to think about it is, you really want to figure out the total area here. You want to figure out the total area here. You want to figure out this t... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
Another way to think about it is, you really want to figure out the total area here. You want to figure out the total area here. You want to figure out this total area. And let me zoom in, and I'll generalize it a little bit. So if you have one circle like that, and then you have another overlapping circle like that, a... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
And let me zoom in, and I'll generalize it a little bit. So if you have one circle like that, and then you have another overlapping circle like that, and you wanted to figure out the total area of the circles combined, you would look at the area of this circle, you would look at the area of this circle, and then you co... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
So in order to only count that area once, you have to subtract that area from the sum. So if this area has A, this area is B, and the intersection where they overlap is C, the combined area is going to be A plus B minus where they overlap, minus C. So that's the same thing over here. We're counting all the jacks, and t... | Probability with playing cards and Venn diagrams Probability and Statistics Khan Academy.mp3 |
After randomization, each child was asked to watch a cartoon in a private room, containing a large bowl of Goldfish crackers. The cartoon included two commercial breaks. The first group watched food commercials, mostly snacks, while the second group watched non-food commercials, games and entertainment products. Once t... | Statistical significance of experiment Probability and Statistics Khan Academy (2).mp3 |
Once the child finished watching the cartoon, the conductors of the experiment weighed the cracker bowls to measure how many grams of crackers the child ate. They found that the mean amount of crackers eaten by the children who watched food commercials is 10 grams greater than the mean amount of crackers eaten by the c... | Statistical significance of experiment Probability and Statistics Khan Academy (2).mp3 |
They took 500 children and then they randomly assigned them to two different groups. So you have group 1 over here and you have group 2. So let's say that this right over here is the first group. The first group watched food commercials. So this is group number 1. So they watched food commercials. We could call this th... | Statistical significance of experiment Probability and Statistics Khan Academy (2).mp3 |
The first group watched food commercials. So this is group number 1. So they watched food commercials. We could call this the treatment group. We're trying to see what's the effect of watching food commercials. And then they tell us the second group watched non-food commercials. So this is the control group. | Statistical significance of experiment Probability and Statistics Khan Academy (2).mp3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.