Sentence stringlengths 101 2.5k | video_title stringlengths 44 104 |
|---|---|
Minus the probability of yellow. I'll write yellow in yellow. Yellow and getting a cube. And so what we've just done here, and you could play with the numbers, the numbers I just used as an example right here to make things a little bit concrete, but you can see this is a generalizable thing. If we have the probability... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
And so what we've just done here, and you could play with the numbers, the numbers I just used as an example right here to make things a little bit concrete, but you can see this is a generalizable thing. If we have the probability of one condition or another condition, so let me rewrite it. The probability, and I'll j... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
This gives us an interesting idea. The probability of getting one condition of an object being a member of set A or a member of set B is equal to the probability that it is a member of set A plus the probability that it is a member of set B minus the probability that it is a member of both. And this is a really useful ... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
I think sometimes it's called the addition rule of probability, but I wanted to show you it's a completely common sense thing. The reason why you can't just add these two probabilities is because they might have some overlap. There's a probability of getting both. And if you just added both of these, you would be doubl... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
And if you just added both of these, you would be double counting that overlap, which we've already seen earlier in this video. So you have to subtract one version of the overlap out so you are not double counting it. And I'll throw one other idea out. Sometimes you have possibilities that have no overlap. So let's say... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Sometimes you have possibilities that have no overlap. So let's say this is a set of all possibilities. And let's say this is a set that meets condition A. Let's say that this is the set that meets condition B. So in this situation, there is no overlap. Nothing is a member of both set A and B. So in this situation, the... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
Let's say that this is the set that meets condition B. So in this situation, there is no overlap. Nothing is a member of both set A and B. So in this situation, the probability of A and B is 0. There is no overlap. And these type of conditions, or these two events, are called mutually exclusive. So if events are mutual... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
So in this situation, the probability of A and B is 0. There is no overlap. And these type of conditions, or these two events, are called mutually exclusive. So if events are mutually exclusive, that means that they both cannot happen at the same time. There's no event that meets both of these conditions. And if things... | Addition rule for probability Probability and Statistics Khan Academy.mp3 |
I have this article right here from WebMD. And the point of this isn't to poke holes at WebMD. I think they have some great articles and they have some great information on their site. But what I want to do here is to think about what a lot of articles you might read or a lot of research you might read are implying and... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
But what I want to do here is to think about what a lot of articles you might read or a lot of research you might read are implying and to think about whether they really imply what they claim to be implying. So this is an excerpt of an article. And the title of the article says, eating breakfast may beat teen obesity.... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So they're already trying to kind of create this cause and effect relationship. The title itself says, if you eat breakfast, then you're less likely or you won't be obese. You're not going to be obese. So the title right there already sets up this, that eating breakfast may beat teen obesity. And then they tell us abou... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So the title right there already sets up this, that eating breakfast may beat teen obesity. And then they tell us about the study. In the study, published in Pediatrics, researchers analyzed the dietary and weight patterns of a group of 2,216 adolescents over a five-year period from public schools in Minneapolis, St. P... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And I won't talk too much about it. This looks like a good sample size. It was over a large period of time. I'll just give the researchers the benefit of the doubt, assume that it was over a broad audience that they were able to control for a lot of variables. But then they go on to say, the researchers write that teen... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
I'll just give the researchers the benefit of the doubt, assume that it was over a broad audience that they were able to control for a lot of variables. But then they go on to say, the researchers write that teens who ate breakfast regularly had a lower percentage of total calories from saturated fat and ate more fiber... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Breakfast tends to be things like cereals, grains, you eat syrup, you eat waffles. That all tends to fall in the category of carbohydrates and sugars. And frankly, that's not even necessarily a good thing. Not obvious to me whether bacon is more or less healthy than downing a bunch of syrup or Froot Loops or whatever e... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Not obvious to me whether bacon is more or less healthy than downing a bunch of syrup or Froot Loops or whatever else. But we'll let that be right here. In addition, regular breakfast eaters seemed more physically active than their breakfast skippers. So over here, they're once again trying to create this other cause a... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So over here, they're once again trying to create this other cause and effect relationship. Regular breakfast eaters seemed more physically active than their breakfast skippers. So the implication here is that breakfast makes you more active. And then this last sentence right over here, they say, over time, researchers... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And then this last sentence right over here, they say, over time, researchers found teens who regularly ate breakfast tended to gain less weight and had a lower body mass index than breakfast skippers. So they're telling us that breakfast skipping, this is the implication here, is more likely or it can be a cause of ma... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Breakfast makes you active. Breakfast skipping will make you obese. So you just say, boy, I have to eat breakfast. And you should always think about the motivations and the industries around things like breakfast. But the more interesting question is, does this research really tell us that eating breakfast can prevent ... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And you should always think about the motivations and the industries around things like breakfast. But the more interesting question is, does this research really tell us that eating breakfast can prevent obesity? Does it really tell us that eating breakfast will cause someone to become more active? Does it really tell... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Does it really tell us that breakfast skipping can make you overweight or make you obese? Or, it is more likely, are they just showing that these two things tend to go together? And this is a really important difference. And let me kind of state slightly technical words here. And they sound fancy, but they really aren'... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And let me kind of state slightly technical words here. And they sound fancy, but they really aren't that fancy. Are they pointing out causality? Are they pointing out causality, which is what it seems like they're implying? Eating breakfast causes you to not be obese. Breakfast causes you to be active. Breakfast skipp... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Are they pointing out causality, which is what it seems like they're implying? Eating breakfast causes you to not be obese. Breakfast causes you to be active. Breakfast skipping causes you to be obese. So it looks like they're kind of implying causality. They're implying cause and effect. But really, what the study loo... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Breakfast skipping causes you to be obese. So it looks like they're kind of implying causality. They're implying cause and effect. But really, what the study looked at is correlation. So the whole point of this is to understand the difference between causality and correlation, because they're saying very different thin... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
But really, what the study looked at is correlation. So the whole point of this is to understand the difference between causality and correlation, because they're saying very different things. Causality versus correlation. And as I said, causality says A causes B. Well, correlation just says A and B tend to be observed... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And as I said, causality says A causes B. Well, correlation just says A and B tend to be observed at the same time. Whenever I see B happening, it looks like A is happening at the same time. Whenever A is happening, it looks like it also tends to happen with B. And the reason why it's super important to notice the dist... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Whenever A is happening, it looks like it also tends to happen with B. And the reason why it's super important to notice the distinction between these is you can come to very, very, very, very different conclusions. So the one thing that this research does do, assuming that it was performed well, is it does show a corr... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So this study does show a correlation. It does show, if we believe all of their data, that breakfast skipping correlates with obesity, and obesity correlates with breakfast skipping. We're seeing it at the same time. Activity correlates with breakfast, and breakfast correlates with activity. All of these correlate. Wel... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Activity correlates with breakfast, and breakfast correlates with activity. All of these correlate. Well, they don't say, and there's no data here that lets me know one way or the other, what is causing what, or maybe you have some underlying cause that is causing both. So for example, they're saying breakfast causes a... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So for example, they're saying breakfast causes activity, or they're implying breakfast causes activity. They're not saying it explicitly. But maybe activity causes breakfast. Maybe. They didn't write the study that people who are active, maybe they're more likely to be hungry in the morning. Activity causes breakfast.... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Maybe. They didn't write the study that people who are active, maybe they're more likely to be hungry in the morning. Activity causes breakfast. And then you start having a different takeaway. Then you don't say, wait, maybe if you're active and you skip breakfast, and I'm not telling you that you should, I have no dat... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And then you start having a different takeaway. Then you don't say, wait, maybe if you're active and you skip breakfast, and I'm not telling you that you should, I have no data one or the other, maybe you'll lose even more weight. Maybe it's even a healthier thing to do. We're not sure. So they're trying to say, look, ... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
We're not sure. So they're trying to say, look, if you have breakfast, it's going to make you active, which is a very positive outcome. But maybe you can have the positive outcome without breakfast. Who knows? Likewise, they say breakfast skipping, or they're implying breakfast skipping can cause obesity. But maybe it'... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Who knows? Likewise, they say breakfast skipping, or they're implying breakfast skipping can cause obesity. But maybe it's the other way around. Maybe people who have high body fat, maybe for whatever reason, they're less likely to get hungry in the morning. So maybe it goes this way. Maybe there's a causality there. O... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Maybe people who have high body fat, maybe for whatever reason, they're less likely to get hungry in the morning. So maybe it goes this way. Maybe there's a causality there. Or even more likely, maybe there's some underlying cause that causes both of these things to happen. And you could think of a bunch of different e... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Or even more likely, maybe there's some underlying cause that causes both of these things to happen. And you could think of a bunch of different examples of that. One could be the physical activity. So physical activity, and these are all just theories. I have no proof for it. But I just want to give you different ways... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So physical activity, and these are all just theories. I have no proof for it. But I just want to give you different ways of thinking about the same data, and maybe not just coming to the same conclusion that this article seems like it's trying to lead us to conclude that we should eat breakfast if we don't want to bec... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So maybe if you're physically active, that leads to you being hungry in the morning. So you're more likely to eat breakfast. And obviously, being physically active also makes it so that you've burned calories, you have more muscle, so that you're not obese. So notice, if you view things this way, if you say physical ac... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So notice, if you view things this way, if you say physical activity is causing both of these, then all of a sudden you lose this connection between breakfast and obesity. Now you can't make the claim that somehow breakfast is the magic formula for someone to not be obese. So let's say that there is an obese person. Le... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Let's say this is the reality, that physical activity is causing both of these things. And let's say that there is an obese person. What will you tell them to do? Will you tell them, eat breakfast and you won't become obese anymore? Well, that might not work, especially if they're not physically active. I mean, what's ... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Will you tell them, eat breakfast and you won't become obese anymore? Well, that might not work, especially if they're not physically active. I mean, what's going to happen if you have an obese person who's not physically active? And then you tell them to eat breakfast. Maybe that'll make things worse. And based on tha... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And then you tell them to eat breakfast. Maybe that'll make things worse. And based on that, the advice or the implication from the article is the wrong thing. Physical activity maybe is the thing that should be focused on. Maybe it's something other than physical activity. Maybe you have sleep. Maybe people who sleep ... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Physical activity maybe is the thing that should be focused on. Maybe it's something other than physical activity. Maybe you have sleep. Maybe people who sleep late, and they're not getting enough sleep, maybe someone who's not getting enough sleep, maybe that leads to obesity. And obviously, because they're not gettin... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
Maybe people who sleep late, and they're not getting enough sleep, maybe someone who's not getting enough sleep, maybe that leads to obesity. And obviously, because they're not getting enough sleep, they wake up as late as possible and they have to run to the next appointment, or they have to run to school in the case ... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So once again, if you find someone's obese, maybe the rule here isn't to force a breakfast down your throat. Maybe it'll become even worse, because maybe it is the lack of sleep that's causing your metabolism to slow down or whatever. So it's very, very important when you're looking at any of these studies to try to sa... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
If it's correlation, you cannot make the judgment that, hey, eating breakfast is necessarily going to make someone less obese. All that tells you is that these things move together. A better study would be one that is able to prove causality. And then we could think of other underlying causes that would kind of break d... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And then we could think of other underlying causes that would kind of break down the narrative that this piece is trying to say. I'm not saying it's wrong. Maybe it's absolutely true that eating breakfast will fight obesity. But I think it's equally or more important to think about what the other causes are, not to jus... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
But I think it's equally or more important to think about what the other causes are, not to just make a blanket statement like that. So for example, maybe poverty causes you to skip breakfast for multiple reasons. Maybe both of your parents are working. There's no one there to give you breakfast. Maybe there's more str... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
There's no one there to give you breakfast. Maybe there's more stress in the family. Who knows what it might be? And so when you have poverty, maybe you're more likely to skip breakfast. And maybe when there's poverty, and maybe you have two, both your parents are working, and the kids have to make their own dinner and... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
And so when you have poverty, maybe you're more likely to skip breakfast. And maybe when there's poverty, and maybe you have two, both your parents are working, and the kids have to make their own dinner and whatever else, maybe they also eat less healthy. So eat less healthy at all times of day, and then that leads to... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
So once again, in this situation, if this is the reality of things, just telling someone to also eat breakfast, regardless of what that breakfast is, even if it's Froot Loops or syrup, that's probably not going to help the situation. Maybe it's just eating unhealthy dinners. Maybe eating unhealthy dinners is the underl... | Correlation and causality Statistical studies Probability and Statistics Khan Academy.mp3 |
We're told that Kai goes to a restaurant that advertises a promotion saying, one in five customers get a free dessert. Suppose Kai goes to the restaurant twice in a given week, and each time he has a 1 5th probability of getting a free dessert. Let X represent the number of free desserts Kai gets in his two trips. Cons... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
Construct the theoretical probability distribution of X. All right, so pause this video and see if you can work through this before we do it together. All right, so first let's just think about the possible values that X could take on. This is the number of free desserts he gets, and he visits twice. So there's some wo... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
This is the number of free desserts he gets, and he visits twice. So there's some world in which he doesn't get any free desserts, so that's zero in his two visits. Maybe on one of the visits, he gets a dessert, and the other one he doesn't. And maybe in both of his visits, he actually is able to get a free dessert. So... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
And maybe in both of his visits, he actually is able to get a free dessert. So he's going to have some place from zero to two free desserts in a given week. So we just have to figure out the probability of each of these. So let's first of all think about the probability, let me write it over here, the probability that ... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
So let's first of all think about the probability, let me write it over here, the probability that capital X is equal to zero is going to be equal to what? Well, that's going to be the probability that he doesn't get a dessert on both days. And it's important to realize that these are independent events. It's not like ... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
It's not like the restaurant's gonna say, oh, if you didn't get a dessert on one day, you're more likely to get it on the other day, or somehow if you got it on a previous day, you're less likely on another day, that they are independent events. So the probability of not getting it on any one day is four out of five. A... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
So four over five times four over five. So the probability that X is equal to zero is going to be 16 25ths, 16 over 25. Now, what about the probability that X is equal to one? What is this going to be? Well, there are two scenarios over here. There's one scenario where let's say on day one, he does not get the dessert,... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
What is this going to be? Well, there are two scenarios over here. There's one scenario where let's say on day one, he does not get the dessert, and on day two, he does get the dessert. But then of course, there's the other scenario where on day one, he gets the dessert, and then on day two, he doesn't get the dessert.... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
But then of course, there's the other scenario where on day one, he gets the dessert, and then on day two, he doesn't get the dessert. These are the two scenarios where he's going to get X equals one. And so if we add these together, let's see, four fifths times one fifth, this is going to be four over 25. And then thi... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
And then this is going to be four over 25 again. And you add these two together, you're going to get eight 25ths. And then last but not least, and actually we could figure out this last one by subtracting 16 and eight from 25, which would actually give us one 25th. But let's just write this out, the probability that X ... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
But let's just write this out, the probability that X equals two, this is the probability he gets a dessert on both days. So one fifth chance on day one, and one fifth chance on the second day. So one fifth times one fifth is one 25th. And you can do a reality check here. These all need to add up to one, and they do in... | Theoretical probability distribution example multiplication Probability & combinatorics.mp3 |
From 15 distinct varieties, Samara will choose three different olive oils and blend them together. A contestant will taste the blend and try to identify which three of the 15 varieties were used to make it. Assume that a contestant can't taste any difference and is randomly guessing. What is the probability that a cont... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
What is the probability that a contestant correctly guesses which three varieties were used? So pause this video and see if you can think about that. And if you can just come up with the expression, you don't have to compute it, that is probably good enough, at least for our purposes. All right, now let's work through ... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
All right, now let's work through this together. So we know several things here. We have 15 distinct varieties, and we are choosing three of those varieties. And anytime we're talking about probability and combinatorics, it's always interesting to say, does order matter? Does it matter what order that Samara is picking... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
And anytime we're talking about probability and combinatorics, it's always interesting to say, does order matter? Does it matter what order that Samara is picking those three from the 15? And it doesn't look like it matters. It looks like we just have to think about what three they are. It doesn't matter what order eit... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
It looks like we just have to think about what three they are. It doesn't matter what order either she picked them in or the order in which the contestant guesses them in. And so if you think about the total number of ways of picking three things from a group of 15, you could write that as 15 choose three. Once again, ... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
Once again, this is just shorthand notation for how many combinations are there so you can pick three things from a group of 15. So some of you might have been tempted to say, hey, let me think about permutations here. And I have 15 things. And from that, I wanna figure out how many ways can I pick three things that ac... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
And from that, I wanna figure out how many ways can I pick three things that actually has order mattering. But this would be the situation where we're talking about the contestant actually having to maybe guess in the same order in which the varieties were originally blended or something like that. But we're not doing ... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
We just care about getting the right three varieties. So this will tell us the total number of ways that you can pick three out of 15. And so what's the probability that the contestant correctly guesses which three varieties were used? Well, the contestant is going to be guessing one out of the possible number of scena... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
Well, the contestant is going to be guessing one out of the possible number of scenarios here. So the probability would be one over 15, choose three. And if you wanted to compute this, this would be equal to one over. Now, how many ways can you pick three things from 15? And of course, there is a formula here, but I al... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
Now, how many ways can you pick three things from 15? And of course, there is a formula here, but I always like to reason through it. Well, you could say, all right, if there's three slots, there's 15 different varieties that could have gone into that first slot. And then there's 14 that could go into that second slot.... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
And then there's 14 that could go into that second slot. And then there's 13 that can go into that third slot. But then we have to remember that it doesn't matter what order we pick them in. So how many ways can you rearrange three things? Well, it would be three factorial or three times two times one. So this would be... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
So how many ways can you rearrange three things? Well, it would be three factorial or three times two times one. So this would be the same thing as three times two times one over 15 times 14 times 13. See, I can simplify this, divide numerator and denominator by two, divide numerator and denominator by three. This is g... | Probability with permutations & combinations example taste testing Probability & combinatorics.mp3 |
So we want to conduct an experiment to test if this pill really can help people lower their blood sugar. So the first thing we need to think about is how do we even measure or test whether people's blood sugar is getting lowered? Well, for our experiment, what's typically done is we measure folks' hemoglobin A1c. You d... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
You don't have to worry too much about this in the context of statistics, but a hemoglobin A1c test is a way that's typically used to measure your average blood sugar over the last three months. And we have whole videos on Khan Academy explaining how that works. So our hope would be that our pill lowers people's blood ... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
Now we have terms for this. The thing that is causing something else to change, we call this the explanatory variable. Explanatory variable. And the thing that might get changed by that explanatory variable, depending on whether you take the pill or not, we call that our response. Response variable. So now let's actual... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
And the thing that might get changed by that explanatory variable, depending on whether you take the pill or not, we call that our response. Response variable. So now let's actually conduct the experiment. So what we would do is we would go to the population, population of diabetics, and we would wanna take a random sa... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
So what we would do is we would go to the population, population of diabetics, and we would wanna take a random sample from that population of diabetics, a reasonably large one, and later in statistics we talk about what a good-sized sample might be. But let's say that we randomly sample, randomly sample 100 folks. So ... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
And then you would want to assign these folks randomly to two different groups. One would be your control group, and this would be the group of people who won't take the new medicine. And then you would have your treatment group. These are the groups of folks who will be given the new medicine, the treatment group. Now... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
These are the groups of folks who will be given the new medicine, the treatment group. Now in some cases you can just randomly assign these 100 folks between these two groups. And one way to do it is you could give all of them a random number between one and 100, and then the top 50 go into treatment, and the bottom 50... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
Now sometimes you might wanna be a little bit more sophisticated than that. For example, there might be evidence that someone's sex might somehow influence how they respond to a drug. So what you could do is something called block design, where let's say this group just happens to have 60 females and 40 males. Well in ... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
Well in block design, you can randomly assign, but you can do it in a way that you can ensure that both of these groups have the same proportions of male and female. So for example, if you have 60 females here, you can ensure that 30 of them end up in the control, and 30 end up in the treatment. But you would assign th... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
Of these 40 males, 20 end up in the control, and 20 end up in the treatment. So once you have folks in both of these groups, what you would probably want to do is measure their A1c at the beginning. You could view that as a baseline. And then over the course of the experiment, you would give the pill to the treatment g... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
And then over the course of the experiment, you would give the pill to the treatment group, and in the control group, you might be saying, oh, we just wouldn't do anything. But the best practice is actually to give a pill that looks just like the real thing to the control group. This is known as a placebo. And the reas... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
And the reason why we do that is there's definitely evidence that when people think they're taking a pill that might help them, that even psychologically, it can have an effect on them, and sometimes it helps them. This is known as the placebo effect. And not only would you give both groups a pill that looks the same, ... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
When you don't tell them which group they are in, that's known as a blind experiment. And you probably also don't wanna tell the people who are administering the experiment which group they are administering, and that's called a double blind. So even the doctors or the nurses that are administering the experiment, when... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
And you might say, well, why is it important for an experiment to be blind or especially double blind? Well, that avoids, one, any type of psychological effect from the point of the patient, or from the, say, the caregivers in this situation. So they don't kind of give it away. They don't tell these folks, hey, you're ... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
They don't tell these folks, hey, you're actually just pretending to take a pill. And so that ensures that we minimize the amount of influence or bias that might happen. You might even have a triple blind experiment where even the folks who are analyzing the eventual data from this experiment don't know whether they're... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
They just compare the two different groups. But anyway, you do, you, people take the medicine and the placebo over the course of the experiment. Maybe this lasts for three months. And then you would wanna measure their A1c later. And then you would see their change in the A1c. Now, if you saw that there wasn't really a... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
And then you would wanna measure their A1c later. And then you would see their change in the A1c. Now, if you saw that there wasn't really a difference in the change in A1c between the control and the treatment group, then you'd say, well, that probably means that my pill didn't work. Now, if you do get a greater reduc... | Impact of mass on orbital speed Study design AP Statistics Khan Academy.mp3 |
For the final round, each of them spin a wheel to determine what star ingredient must be in their dish. I guess the primary ingredient, and we can see it could be chard, spinach, romaine, lettuce, I'm guessing, cabbage, arugula, or kale. And so then they give us these different types of events, or at least the symbols ... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
So K sub one means the first contestant lands on kale. K sub two means the second contestant lands on kale. K sub one with this superscript C, which we could view as complement. So K sub one complement, the first contestant does not land on kale. So it's the complement of this one right over here. And then K sub two co... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
So K sub one complement, the first contestant does not land on kale. So it's the complement of this one right over here. And then K sub two complement would be that the second contestant does not land on kale. So the not of K sub two right over here. Using the general multiplication rule, express symbolically the proba... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
So the not of K sub two right over here. Using the general multiplication rule, express symbolically the probability that neither contestant lands on kale. So pause this video and see if you can have a go at this. All right. So the general multiplication rule is just saying this notion that the probability of two event... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
All right. So the general multiplication rule is just saying this notion that the probability of two events, A and B, is going to be equal to the probability of, let's say A given B, times the probability of B. Now, if they're independent events, if the probability of A occurring does not depend in any way on whether B... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
And so if you have two independent events, you would just multiply their probabilities. So that's just all they're talking about, the general multiplication rule. But let me express what they're actually asking us to express, the probability that neither contestant lands on kale. So that means that this is going to hap... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
So that means that this is going to happen. The first contestant does not land on kale, and this is going to happen. The second contestant does not land on kale. So I could write it this way. The probability that K sub one complement and K sub two complement, and I could write it this way. This is going to be equal to,... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
So I could write it this way. The probability that K sub one complement and K sub two complement, and I could write it this way. This is going to be equal to, we know that these are independent events because if the first contestant gets kale or whatever they get, it doesn't get taken out of the running for the second ... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
The second contestant still has an equal probability of getting or not getting kale, regardless of what happened for the first contestant. So that means we're just in the situation where we multiply these probabilities. So that's going to be the probability of K sub one complement times the probability of K sub two com... | Interpreting general multiplication rule Probability & combinatorics (2).mp3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.