title

Lecture 6: Monty Hall, Simpson's Paradox | Statistics 110

description

We show how conditional probability sheds light on two of the most famous puzzles in statistics, both of which are often counterintuitive (at first): the Monty Hall problem and Simpson's paradox.

detail

{'title': "Lecture 6: Monty Hall, Simpson's Paradox | Statistics 110", 'heatmap': [{'end': 710.018, 'start': 673.558, 'weight': 0.726}, {'end': 1188.558, 'start': 1116.098, 'weight': 1}], 'summary': "This lecture series covers the monty hall problem, exploring conditional probability, tree diagrams, and the counterintuitive nature of the scenario, concluding that switching doors gives a two-thirds chance of success. it also delves into simpson's paradox, illustrating how aggregated data can lead to paradoxical conclusions, challenging common understanding of inequalities and aggregates.", 'chapters': [{'end': 72.421, 'segs': [{'end': 26.614, 'src': 'embed', 'start': 0.089, 'weight': 0, 'content': [{'end': 6.098, 'text': "So we're talking about conditional probability, right? We're continuing to do conditional probability.", 'start': 0.089, 'duration': 6.009}, {'end': 14.35, 'text': "And so today we're gonna talk about a couple of the most interesting famous problems related to conditional probability.", 'start': 6.719, 'duration': 7.631}, {'end': 15.432, 'text': 'First one.', 'start': 14.931, 'duration': 0.501}, {'end': 24.012, 'text': "A lot of you have seen it in some form or other, and that's called the Monty Hall problem, the three-door problem.", 'start': 16.887, 'duration': 7.125}, {'end': 26.614, 'text': 'Very, very famous problem.', 'start': 24.212, 'duration': 2.402}], 'summary': 'Discussing famous problems related to conditional probability.', 'duration': 26.525, 'max_score': 0.089, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ89.jpg'}, {'end': 79.324, 'src': 'embed', 'start': 48.372, 'weight': 1, 'content': [{'end': 53.473, 'text': "And we'll approach it from more than one perspective, because it's a very subtle problem.", 'start': 48.372, 'duration': 5.101}, {'end': 61.016, 'text': 'And this is the sort of problem that almost everyone gets wrong the first time they see it, and If they think about it for a while,', 'start': 53.533, 'duration': 7.483}, {'end': 62.256, 'text': 'they think they understand it.', 'start': 61.016, 'duration': 1.24}, {'end': 69.459, 'text': 'And then you ask the same question just in a slight disguise, and then everyone gets it wrong again.', 'start': 62.716, 'duration': 6.743}, {'end': 72.421, 'text': "So I'm gonna try to talk a lot about.", 'start': 69.479, 'duration': 2.942}, {'end': 79.324, 'text': "how do you really think about this, so that you won't get fooled if I ask the same thing and then just change a few things around?", 'start': 72.421, 'duration': 6.903}], 'summary': 'Addressing a tricky problem that often leads to misconceptions and requires a shifted perspective for accurate understanding.', 'duration': 30.952, 'max_score': 48.372, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ48372.jpg'}], 'start': 0.089, 'title': 'Conditional probability problems', 'summary': 'Delves into the monty hall problem, a well-known conditional probability problem featured in popular media. it aims to offer fresh perspectives and insights to aid in comprehending the deceptive nature of the problem.', 'chapters': [{'end': 72.421, 'start': 0.089, 'title': 'Conditional probability problems', 'summary': 'Discusses the monty hall problem, a famous conditional probability problem, which has been widely featured in movies, tv shows, and articles. it aims to provide additional perspectives and insights to help understand the problem, which is known to deceive many upon initial encounter.', 'duration': 72.332, 'highlights': ['The Monty Hall problem is a famous conditional probability problem that has been featured in movies, TV shows, and articles, and there are entire books written about it.', 'The problem is known for deceiving almost everyone upon initial encounter, and even those who think they understand it can be misled when the question is presented in a slightly different manner.', 'The chapter aims to provide additional ways to think about the Monty Hall problem and approach it from more than one perspective to help understand its subtleties.']}], 'duration': 72.332, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ89.jpg', 'highlights': ['The Monty Hall problem is a famous conditional probability problem that has been featured in various media.', 'The problem is known for deceiving almost everyone upon initial encounter.', 'The chapter aims to provide additional ways to think about the Monty Hall problem and approach it from more than one perspective.']}, {'end': 418.73, 'segs': [{'end': 170.501, 'src': 'embed', 'start': 133.757, 'weight': 0, 'content': [{'end': 139.902, 'text': 'Monty Hall asks you to choose a door, okay? So say you pick that one.', 'start': 133.757, 'duration': 6.145}, {'end': 143.865, 'text': 'And so there are a lot of assumptions in this problem.', 'start': 140.642, 'duration': 3.223}, {'end': 147.528, 'text': "We're supposed to assume that one door has a car behind it.", 'start': 144.505, 'duration': 3.023}, {'end': 152.474, 'text': 'The other two doors have goats.', 'start': 149.773, 'duration': 2.701}, {'end': 161.077, 'text': "So you don't know which one.", 'start': 158.636, 'duration': 2.441}, {'end': 162.558, 'text': 'One of these has a car behind it.', 'start': 161.177, 'duration': 1.381}, {'end': 163.598, 'text': 'The other two have goats.', 'start': 162.578, 'duration': 1.02}, {'end': 170.501, 'text': "And we're assuming that you, the contestant, have no idea which one has the car.", 'start': 164.478, 'duration': 6.023}], 'summary': 'Monty hall problem: choose 1 of 3 doors, 1 car, 2 goats. uncertainty for contestant.', 'duration': 36.744, 'max_score': 133.757, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ133757.jpg'}, {'end': 277.545, 'src': 'embed', 'start': 253.567, 'weight': 1, 'content': [{'end': 259.872, 'text': "Monty Hall gives you the option of do you wanna switch to the other door that's unopened or keep your original choice?", 'start': 253.567, 'duration': 6.305}, {'end': 262.795, 'text': 'The question is is it beneficial to switch??', 'start': 260.273, 'duration': 2.522}, {'end': 264.216, 'text': "Okay, so that's the problem.", 'start': 263.235, 'duration': 0.981}, {'end': 274.803, 'text': "And there's one more assumption, which is that Monty always opens, he's always gonna offer you that choice.", 'start': 264.656, 'duration': 10.147}, {'end': 277.545, 'text': "So he's always gonna open a goat door.", 'start': 275.063, 'duration': 2.482}], 'summary': 'Monty hall problem: should you switch doors? assumption: monty always opens a goat door.', 'duration': 23.978, 'max_score': 253.567, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ253567.jpg'}], 'start': 72.421, 'title': 'Monty hall problem', 'summary': 'Discusses the monty hall problem, a game show scenario involving three doors, where a contestant must choose one door to win a car, with relevant assumptions and implications. it also explores if it is beneficial to switch or keep the original choice, assuming monty always opens a door with a goat, and concludes that you should switch doors under certain assumptions.', 'chapters': [{'end': 225.967, 'start': 72.421, 'title': 'Monty hall problem', 'summary': 'Discusses the monty hall problem, a game show scenario involving three doors, where a contestant must choose one door to win a car, with relevant assumptions and implications.', 'duration': 153.546, 'highlights': ["Monty Hall problem involves a game show scenario with three doors, where one door has a car and the other two have goats, and the contestant must choose a door without knowing what's behind it.", "The problem assumes that the contestant wants the car and not the goats, while Monty Hall knows the location of the car and the goats, leading to implications for the contestant's decision-making process.", 'The assumptions in the problem include the contestant having no prior knowledge of the door contents, all doors being equally likely, and Monty Hall being aware of which door has the car.']}, {'end': 301.292, 'start': 225.987, 'title': 'Monty hall problem', 'summary': 'Discusses the monty hall problem, where a player selects a door and is then given the option to switch to another unopened door, considering if it is beneficial to switch or keep the original choice, assuming monty always opens a door with a goat.', 'duration': 75.305, 'highlights': ['Monty always opens a door with a goat, and the player is given the option to switch to another unopened door. Monty always opens a door with a goat, giving the player the option to switch to another unopened door, potentially affecting the chances of winning the car.', 'The player has to decide if it is beneficial to switch from the original choice to the other unopened door. The player needs to evaluate if switching from the original choice to the other unopened door is beneficial in increasing the chances of winning the car.', "Monty needs to ensure that he always opens a door with a goat to avoid spoiling the game. Monty's role is crucial as he needs to ensure that he always opens a door with a goat to avoid spoiling the game, making his choice critical in the process."]}, {'end': 418.73, 'start': 303.834, 'title': 'Monty hall problem and probability', 'summary': 'Discusses the monty hall problem, where monty has the choice of which door to open with equal probabilities, leading to the conclusion that you should switch doors under these assumptions.', 'duration': 114.896, 'highlights': ['The chapter discusses the Monty Hall problem, where Monty has the choice of which door to open with equal probabilities, leading to the conclusion that you should switch doors under these assumptions.', 'Controversy has raged about this problem for years and years and years, partly due to people not understanding probability and the implicit nature of key assumptions.', "On the strategic problems, a new homework and strategic practice have been posted, including a problem that is an extension to the case of 'lazy Monty Hall' where he prefers opening one door to another based on probabilities.", 'Sometimes Monty has a choice of opening doors with different probabilities, and the question arises whether one should switch doors based on his choice.']}], 'duration': 346.309, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ72421.jpg', 'highlights': ["Monty Hall problem involves a game show scenario with three doors, where one door has a car and the other two have goats, and the contestant must choose a door without knowing what's behind it.", 'Monty always opens a door with a goat, and the player is given the option to switch to another unopened door.', 'The chapter discusses the Monty Hall problem, where Monty has the choice of which door to open with equal probabilities, leading to the conclusion that you should switch doors under these assumptions.']}, {'end': 915.935, 'segs': [{'end': 457.029, 'src': 'embed', 'start': 418.97, 'weight': 0, 'content': [{'end': 421.771, 'text': 'And if you switch, your probability of success is two-thirds.', 'start': 418.97, 'duration': 2.801}, {'end': 428.015, 'text': "And if you stick with your original choice, your probability of success is one-third, so it's better to switch.", 'start': 422.392, 'duration': 5.623}, {'end': 428.755, 'text': "It's not 50-50.", 'start': 428.095, 'duration': 0.66}, {'end': 435.379, 'text': "It's sort of like an abuse of the naive definition of probability, I'd say.", 'start': 428.855, 'duration': 6.524}, {'end': 439.241, 'text': "If you just immediately say well, it's 50-50 because there's two doors and we don't know which is which?", 'start': 435.599, 'duration': 3.642}, {'end': 441.302, 'text': "well, that's the naive definition, right?", 'start': 439.241, 'duration': 2.061}, {'end': 442.783, 'text': "Assuming they're equally likely.", 'start': 441.562, 'duration': 1.221}, {'end': 444.324, 'text': 'but why are they equally likely?', 'start': 442.783, 'duration': 1.541}, {'end': 447.145, 'text': "We don't know that they're equally likely, given the evidence.", 'start': 445.004, 'duration': 2.141}, {'end': 452.928, 'text': "We are assuming that initially, I didn't write this, but I said it.", 'start': 448.125, 'duration': 4.803}, {'end': 457.029, 'text': "Initially it's 1 third, 1 third, 1 third as the probabilities, okay?", 'start': 453.228, 'duration': 3.801}], 'summary': 'Switching increases probability of success to two-thirds, better than sticking with original choice.', 'duration': 38.059, 'max_score': 418.97, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ418970.jpg'}, {'end': 590.193, 'src': 'embed', 'start': 539.142, 'weight': 3, 'content': [{'end': 544.587, 'text': "So we're not just conditioning on there being a goat there, we're conditioning on the fact that Monty Hall opened door two.", 'start': 539.142, 'duration': 5.445}, {'end': 556.316, 'text': 'So we have to kinda see why is that relevant, why does it become two thirds? Okay, door two.', 'start': 545.728, 'duration': 10.588}, {'end': 560.42, 'text': 'All right, so I wanna approach this problem in a couple different ways.', 'start': 557.437, 'duration': 2.983}, {'end': 567.417, 'text': 'Maybe three different ways, one intuitive, one with a tree, and one with a probability calculation.', 'start': 562.492, 'duration': 4.925}, {'end': 570.46, 'text': 'Okay, actually two intuitive ways.', 'start': 568.798, 'duration': 1.662}, {'end': 573.263, 'text': 'There are a lot of ways to think about this problem, but some of them are wrong.', 'start': 570.64, 'duration': 2.623}, {'end': 575.545, 'text': "So I'm gonna show you some correct ways to think about this.", 'start': 573.423, 'duration': 2.122}, {'end': 581.791, 'text': 'So first of all, a tree diagram I think is a very good way to picture this problem.', 'start': 576.666, 'duration': 5.125}, {'end': 585.775, 'text': "So let's draw a tree.", 'start': 582.912, 'duration': 2.863}, {'end': 590.193, 'text': 'So you choose the door.', 'start': 588.911, 'duration': 1.282}], 'summary': 'Exploring the monty hall problem through various approaches and diagrams.', 'duration': 51.051, 'max_score': 539.142, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ539142.jpg'}, {'end': 710.018, 'src': 'heatmap', 'start': 673.558, 'weight': 0.726, 'content': [{'end': 682.163, 'text': "Then he opens door two or door three, and we're assuming those are equally likely, so I'm putting one half, one half on those branches.", 'start': 673.558, 'duration': 8.605}, {'end': 691.769, 'text': 'Now, if we pick door one and the car is behind door two, then Monty Hall has no choice but to open door three right?', 'start': 682.784, 'duration': 8.985}, {'end': 696.776, 'text': "And then he'll offer you do you wanna switch to door two or not?", 'start': 693.055, 'duration': 3.721}, {'end': 698.856, 'text': 'So in this case he has no choice.', 'start': 697.276, 'duration': 1.58}, {'end': 700.036, 'text': 'so this has probability one.', 'start': 698.856, 'duration': 1.18}, {'end': 704.257, 'text': 'And then, lastly, we pick door one.', 'start': 701.096, 'duration': 3.161}, {'end': 705.637, 'text': 'car is behind door three.', 'start': 704.257, 'duration': 1.38}, {'end': 710.018, 'text': 'Monty Hall has no choice but to open door two to reveal a goat right?', 'start': 705.637, 'duration': 4.381}], 'summary': 'Analyzing monty hall problem probabilities and outcomes.', 'duration': 36.46, 'max_score': 673.558, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ673558.jpg'}, {'end': 876.039, 'src': 'embed', 'start': 842.444, 'weight': 5, 'content': [{'end': 855.614, 'text': 'was that the probability of success if switching, given that Monty, because I was assuming he opened door two?', 'start': 842.444, 'duration': 13.17}, {'end': 862.156, 'text': 'And we just showed just by this tree diagram that this is equal to 2 thirds.', 'start': 856.274, 'duration': 5.882}, {'end': 865.237, 'text': 'Of course you could do the same thing.', 'start': 863.896, 'duration': 1.341}, {'end': 873.319, 'text': "if he opens door three, just circle the other two same thing again and it's still 2 thirds, okay?", 'start': 865.237, 'duration': 8.082}, {'end': 876.039, 'text': "So that's one way to think of it.", 'start': 873.339, 'duration': 2.7}], 'summary': 'The probability of success when switching is 2/3, regardless of which door monty opens.', 'duration': 33.595, 'max_score': 842.444, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ842444.jpg'}, {'end': 925.834, 'src': 'embed', 'start': 898.129, 'weight': 6, 'content': [{'end': 905.566, 'text': 'The other two thirds of the time, Your initial guess is wrong, Monte opens up a goat door and then you should switch.', 'start': 898.129, 'duration': 7.437}, {'end': 911.911, 'text': "So two thirds of the time you should switch, I mean, you should always switch cuz two thirds of the time you'll get it right and the other one third.", 'start': 905.626, 'duration': 6.285}, {'end': 915.935, 'text': "The one third where you're getting it right is where you were initially correct, but that's only one third of the time.", 'start': 911.951, 'duration': 3.984}, {'end': 925.834, 'text': "Okay, so that's the tree diagram which I think is useful, but it's also useful to just see how can we do this as a conditional probability argument.", 'start': 917.688, 'duration': 8.146}], 'summary': 'Switching doors increases chances of winning by two-thirds.', 'duration': 27.705, 'max_score': 898.129, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ898129.jpg'}], 'start': 418.97, 'title': 'The monty hall problem', 'summary': 'Delves into the monty hall problem, explaining the probability of success when switching or sticking with the original choice, and the use of tree diagrams to calculate conditional probabilities, concluding that switching doors gives a two-thirds chance of success.', 'chapters': [{'end': 590.193, 'start': 418.97, 'title': 'Monty hall problem', 'summary': "Discusses the monty hall problem, explaining the probability of success when switching or sticking with the original choice and the abuse of the naive definition of probability. it also delves into the conditional probability and the relevance of the evidence, ultimately leading to the conclusion that it's better to switch with a probability of success of two-thirds compared to one-third for sticking with the original choice.", 'duration': 171.223, 'highlights': ['The probability of success when switching is two-thirds, while sticking with the original choice yields a probability of success of one-third, demonstrating the favorable outcome of switching.', 'The chapter emphasizes the abuse of the naive definition of probability, highlighting the misconception of assuming 50-50 probability due to the presence of two doors without considering the evidence, raising the question of why they are assumed to be equally likely.', 'It explains the initial probabilities of 1 third, 1 third, 1 third and how these probabilities change after observing the evidence, debunking the misconception of conditional probabilities and emphasizing the significance of considering all the evidence for accurate conditioning.', 'The relevance of Monty opening door two and the presence of a goat behind it is discussed, emphasizing the need to condition on all the evidence and not just the presence of a goat, ultimately leading to the conclusion that the probability of success is two-thirds when switching due to the specific evidence presented.', 'The chapter suggests multiple approaches to understanding the problem, including an intuitive approach, a tree diagram, and a probability calculation, while cautioning against incorrect ways of reasoning and presenting correct methodologies for solving the Monty Hall problem.']}, {'end': 915.935, 'start': 591.696, 'title': 'Monty hall problem analysis', 'summary': 'Discusses the monty hall problem and demonstrates the use of tree diagrams to calculate conditional probabilities, concluding that switching doors gives a two-thirds chance of success.', 'duration': 324.239, 'highlights': ['The probability of success if switching, given that Monty Hall opened door 2, is 2 thirds, illustrating the advantage of switching doors in the Monty Hall problem.', 'The tree diagram is used to calculate conditional probabilities, with a demonstration of multiplying and renormalizing probabilities to show that switching doors gives a two-thirds chance of success.', 'The analysis concludes that two-thirds of the time, switching doors provides the correct answer in the Monty Hall problem, indicating the benefit of switching doors in this scenario.', 'The chapter explains the intuitive understanding that two-thirds of the time, switching doors results in success in the Monty Hall problem, emphasizing the strategic advantage of switching doors over sticking with the initial choice.']}], 'duration': 496.965, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ418970.jpg', 'highlights': ['Switching yields a 2/3 probability of success, while sticking yields 1/3.', 'The abuse of the naive definition of probability is emphasized, questioning the assumption of equal likelihood.', 'Initial probabilities of 1/3, 1/3, 1/3 change after observing evidence, debunking misconceptions.', 'The relevance of Monty opening door two and the presence of a goat behind it is discussed.', 'The chapter suggests multiple approaches to understanding the problem, cautioning against incorrect reasoning.', 'The tree diagram is used to calculate conditional probabilities, demonstrating the advantage of switching doors.', 'The analysis concludes that two-thirds of the time, switching doors provides the correct answer.', 'The intuitive understanding that two-thirds of the time, switching doors results in success is explained.']}, {'end': 1290.408, 'segs': [{'end': 989.472, 'src': 'embed', 'start': 917.688, 'weight': 0, 'content': [{'end': 925.834, 'text': "Okay, so that's the tree diagram which I think is useful, but it's also useful to just see how can we do this as a conditional probability argument.", 'start': 917.688, 'duration': 8.146}, {'end': 931.899, 'text': "You can do this problem using Bayes' rule, but actually I would prefer to just use the law of total probability here.", 'start': 926.575, 'duration': 5.324}, {'end': 939.144, 'text': "So let's do this using the law of total probability, LOTP.", 'start': 934.64, 'duration': 4.504}, {'end': 948.7, 'text': "When we're using law of total probability, the key step is deciding what to condition on.", 'start': 942.779, 'duration': 5.921}, {'end': 960.362, 'text': "okay?. And one of the really nice things about statistics and probability that's basically unique to this subject is with most mathematical subjects,", 'start': 948.7, 'duration': 11.662}, {'end': 964.243, 'text': "if you have a problem and you're stuck right?", 'start': 960.362, 'duration': 3.881}, {'end': 968.704, 'text': "You can't just say well, I wish that I knew this and I wish that I knew that.", 'start': 964.263, 'duration': 4.441}, {'end': 976.121, 'text': "Well, you can say that, but it doesn't help you, right? In probability, you think like, I wish I knew this, I wish I knew that.", 'start': 968.904, 'duration': 7.217}, {'end': 978.463, 'text': "That's giving you a hint as to what you should condition on.", 'start': 976.181, 'duration': 2.282}, {'end': 982.566, 'text': 'Then you just condition on it and you act as if you did know that.', 'start': 978.483, 'duration': 4.083}, {'end': 989.472, 'text': "okay?. So I didn't name the law of total probability, but if I had, I would have just called it wishful thinking, right?", 'start': 982.566, 'duration': 6.906}], 'summary': 'Using law of total probability to solve problems, emphasizing conditional probability', 'duration': 71.784, 'max_score': 917.688, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ917688.jpg'}, {'end': 1188.558, 'src': 'heatmap', 'start': 1116.098, 'weight': 1, 'content': [{'end': 1123.541, 'text': "But P of D1 is the prior probability that door 1 has the car, and we're assuming that they're all equally likely to start with.", 'start': 1116.098, 'duration': 7.443}, {'end': 1125.842, 'text': "So it's just 1 3rd, 1 3rd, 1 3rd for these weights.", 'start': 1123.561, 'duration': 2.281}, {'end': 1134.927, 'text': "Okay, now what's this? D1, I'm just assuming that, remember, we're assuming that we picked door 1.", 'start': 1127.663, 'duration': 7.264}, {'end': 1139.208, 'text': 'So that means we got it right initially, but we switched.', 'start': 1134.927, 'duration': 4.281}, {'end': 1139.949, 'text': "So that's bad.", 'start': 1139.328, 'duration': 0.621}, {'end': 1140.729, 'text': 'This is a bad case.', 'start': 1139.989, 'duration': 0.74}, {'end': 1141.79, 'text': 'So this is going to be 0.', 'start': 1140.769, 'duration': 1.021}, {'end': 1143.11, 'text': "It's never going to work in that case.", 'start': 1141.79, 'duration': 1.32}, {'end': 1146.552, 'text': 'Now in this case, we picked door 1.', 'start': 1143.83, 'duration': 2.722}, {'end': 1149.113, 'text': 'The car is behind door 2.', 'start': 1146.552, 'duration': 2.561}, {'end': 1151.614, 'text': 'Monty Hall will open door 3, and we should switch.', 'start': 1149.113, 'duration': 2.501}, {'end': 1155.429, 'text': 'So we have probability of success 1 here, 1 times 1 third.', 'start': 1152.366, 'duration': 3.063}, {'end': 1157.911, 'text': "Similarly, in this case, it's gonna work.", 'start': 1155.789, 'duration': 2.122}, {'end': 1161.533, 'text': "So that's also 1 equals 2 thirds.", 'start': 1158.051, 'duration': 3.482}, {'end': 1170.12, 'text': "So it's actually a very easy calculation, right? Because these probabilities are very, very easy to compute once we know where the car is.", 'start': 1163.075, 'duration': 7.045}, {'end': 1171.341, 'text': "So it's 2 thirds.", 'start': 1170.4, 'duration': 0.941}, {'end': 1181.072, 'text': "There's one slightly subtle point here, which is that this is the unconditional probability that our strategy will be successful.", 'start': 1173.305, 'duration': 7.767}, {'end': 1188.558, 'text': 'And you could say well, what if we wanted the conditional probability, given that Monty Hall opened door two?', 'start': 1181.432, 'duration': 7.126}], 'summary': 'Probability of success in monty hall problem is 2/3 due to conditional probabilities and switching doors.', 'duration': 72.46, 'max_score': 1116.098, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1116098.jpg'}, {'end': 1188.558, 'src': 'embed', 'start': 1163.075, 'weight': 3, 'content': [{'end': 1170.12, 'text': "So it's actually a very easy calculation, right? Because these probabilities are very, very easy to compute once we know where the car is.", 'start': 1163.075, 'duration': 7.045}, {'end': 1171.341, 'text': "So it's 2 thirds.", 'start': 1170.4, 'duration': 0.941}, {'end': 1181.072, 'text': "There's one slightly subtle point here, which is that this is the unconditional probability that our strategy will be successful.", 'start': 1173.305, 'duration': 7.767}, {'end': 1188.558, 'text': 'And you could say well, what if we wanted the conditional probability, given that Monty Hall opened door two?', 'start': 1181.432, 'duration': 7.126}], 'summary': 'Probability of winning is 2/3 when using a specific strategy.', 'duration': 25.483, 'max_score': 1163.075, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1163075.jpg'}, {'end': 1290.408, 'src': 'embed', 'start': 1251.694, 'weight': 4, 'content': [{'end': 1258.275, 'text': 'Because in that problem, I said that Monty Hall is too lazy to walk over and open door three unless he has to, or that kind of thing.', 'start': 1251.694, 'duration': 6.581}, {'end': 1259.775, 'text': "Then there's an asymmetry.", 'start': 1258.675, 'duration': 1.1}, {'end': 1264.897, 'text': "But in this version, it's symmetrical, so conditional and unconditional works the same way.", 'start': 1260.276, 'duration': 4.621}, {'end': 1266.837, 'text': 'So, okay, so we get two-thirds.', 'start': 1265.497, 'duration': 1.34}, {'end': 1270.118, 'text': "And they're nice, you can easily find applets online.", 'start': 1267.717, 'duration': 2.401}, {'end': 1274.439, 'text': 'I put a link on the webpage for a nice one that the New York Times has if you wanted to try it out.', 'start': 1270.138, 'duration': 4.301}, {'end': 1280.622, 'text': "There's one thing that So, just to tell you a little bit about the controversy over this problem.", 'start': 1274.999, 'duration': 5.623}, {'end': 1290.408, 'text': 'that controversy started raging when Marilyn Vos Savant, who writes a column in Parade magazine, someone wrote in and asked this question.', 'start': 1280.622, 'duration': 9.786}], 'summary': 'Monty hall problem has a symmetrical version, yielding a two-thirds chance, sparking controversy.', 'duration': 38.714, 'max_score': 1251.694, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1251694.jpg'}], 'start': 917.688, 'title': 'Probability and conditional probability', 'summary': 'Discusses the law of total probability and conditional probability, emphasizing the importance of specific information for conditioning. it also explains the monty hall problem and its probabilities, highlighting the controversy surrounding it.', 'chapters': [{'end': 1021.042, 'start': 917.688, 'title': 'Law of total probability for conditional probability', 'summary': 'Discusses the concept of conditioning in the law of total probability to solve probability problems, emphasizing the importance of wishing for specific information to condition on, with a focus on determining conditional probabilities.', 'duration': 103.354, 'highlights': ['The key step in using the law of total probability is deciding what to condition on, with the unique aspect of probability being the ability to use wishful thinking to determine the conditioning variable.', 'In probability problems, wishing for specific information provides a hint as to what to condition on, such as wishing to know the location of the car in a given scenario.', "The law of total probability, LOTP, is preferred over Bayes' rule for solving the problem at hand."]}, {'end': 1290.408, 'start': 1021.262, 'title': 'Monty hall problem', 'summary': 'Explains the probability calculation of success in the monty hall problem using the switching strategy, demonstrating that the unconditional and conditional probabilities of success are both 2 thirds, with a mention of the controversy surrounding the problem.', 'duration': 269.146, 'highlights': ['The unconditional and conditional probability of success in the Monty Hall problem using the switching strategy are both 2 thirds. The probability calculation of success in the Monty Hall problem using the switching strategy results in both the unconditional and conditional probabilities of success being 2 thirds.', 'Mention of the controversy surrounding the Monty Hall problem. The transcript briefly discusses the controversy surrounding the Monty Hall problem, which began when Marilyn Vos Savant, who writes a column in Parade magazine, received a question about it.', 'Link to online applets for trying out the Monty Hall problem. There is a mention of the availability of applets online, including a link to a New York Times applet provided on the webpage for trying out the Monty Hall problem.']}], 'duration': 372.72, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ917688.jpg', 'highlights': ["The law of total probability, LOTP, is preferred over Bayes' rule for solving the problem at hand.", 'In probability problems, wishing for specific information provides a hint as to what to condition on, such as wishing to know the location of the car in a given scenario.', 'The key step in using the law of total probability is deciding what to condition on, with the unique aspect of probability being the ability to use wishful thinking to determine the conditioning variable.', 'The unconditional and conditional probability of success in the Monty Hall problem using the switching strategy are both 2 thirds.', 'Mention of the controversy surrounding the Monty Hall problem. The transcript briefly discusses the controversy surrounding the Monty Hall problem, which began when Marilyn Vos Savant, who writes a column in Parade magazine, received a question about it.', 'Link to online applets for trying out the Monty Hall problem. There is a mention of the availability of applets online, including a link to a New York Times applet provided on the webpage for trying out the Monty Hall problem.']}, {'end': 1606.653, 'segs': [{'end': 1464.996, 'src': 'embed', 'start': 1366.142, 'weight': 0, 'content': [{'end': 1371.063, 'text': "So I don't understand how people will still continue to argue with that.", 'start': 1366.142, 'duration': 4.921}, {'end': 1377.505, 'text': "when you just try it out, simulate it, you'll see two thirds of the time you succeed by switching.", 'start': 1371.063, 'duration': 6.442}, {'end': 1379.885, 'text': "I mean, it's just kind of mind boggling.", 'start': 1377.585, 'duration': 2.3}, {'end': 1388.347, 'text': "But maybe some of the math PhDs didn't wanna actually try it out cuz they thought that they proved that it was one half or something.", 'start': 1380.945, 'duration': 7.402}, {'end': 1391.388, 'text': "Anyway, so that's the Monty Hall problem.", 'start': 1389.327, 'duration': 2.061}, {'end': 1396.57, 'text': "I wanted to mention one other intuition for this that's kind of unusual.", 'start': 1392.348, 'duration': 4.222}, {'end': 1403.813, 'text': 'Usually, when we have a complicated problem, the suggestion would be look at a simpler case, right?', 'start': 1397.25, 'duration': 6.563}, {'end': 1410.155, 'text': "But I did emphasize the fact that it's useful to consider simple and extreme cases, right?", 'start': 1404.833, 'duration': 5.322}, {'end': 1419.619, 'text': 'So an extreme case here would be what if, instead of three doors, what if we considered the Monty Hall problem with a million doors??', 'start': 1410.575, 'duration': 9.044}, {'end': 1431.924, 'text': 'So you pick one of those 1 million doors and then Monty Hall proceeds to open 999, 998 doors, leaving just one door should you switch?', 'start': 1420.799, 'duration': 11.125}, {'end': 1442.363, 'text': "In that case, I've never met anyone who would not switch, right? Well, I've never met anyone like that.", 'start': 1433.324, 'duration': 9.039}, {'end': 1447.594, 'text': "Because with a million doors, you're extremely confident that your initial guess is wrong.", 'start': 1443.546, 'duration': 4.048}, {'end': 1451.021, 'text': "And you're extremely confident that that one remaining door has the car.", 'start': 1447.995, 'duration': 3.026}, {'end': 1454.808, 'text': "Conceptually though, there's no difference between that and this.", 'start': 1451.806, 'duration': 3.002}, {'end': 1458.731, 'text': "It's like three doors or a million doors.", 'start': 1455.589, 'duration': 3.142}, {'end': 1464.996, 'text': 'The argument for one half, one half here would apply in the same way with a million doors.', 'start': 1460.253, 'duration': 4.743}], 'summary': 'Simulating the monty hall problem shows 2/3 success rate by switching doors, even with a million doors.', 'duration': 98.854, 'max_score': 1366.142, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1366142.jpg'}], 'start': 1293.47, 'title': "Monty hall problem & simpson's paradox", 'summary': "Explores the monty hall problem and simpson's paradox, showcasing the role of conditional probability and the counterintuitive nature of these scenarios, challenging common intuition and demonstrating their impact on decision-making.", 'chapters': [{'end': 1410.155, 'start': 1293.47, 'title': 'The monty hall problem and conditional probability', 'summary': 'Discusses the monty hall problem, where despite initial misunderstandings, the correct answer can be obtained through conditional probability and simple simulations, challenging the intuition of many, including math phds.', 'duration': 116.685, 'highlights': ['The Monty Hall problem demonstrates the importance of conditional probability in obtaining the correct answer, despite the initial widespread misunderstanding.', 'Simple simulations, such as trying it out 1,000 times via computer simulation, clearly show that two-thirds of the time one succeeds by switching, challenging the intuition of many, including math PhDs.', 'The chapter emphasizes the utility of considering simple and extreme cases, contrasting with the usual approach of looking at a simpler case for complicated problems.']}, {'end': 1606.653, 'start': 1410.575, 'title': "Monty hall problem & simpson's paradox", 'summary': "Discusses the monty hall problem with a million doors and the counterintuitive nature of simpson's paradox, illustrating the importance of conditional thinking and the potential for initial intuition to lead to incorrect conclusions.", 'duration': 196.078, 'highlights': ["The counterintuitive nature of Simpson's Paradox is emphasized, as it is a problem where most people initially find it impossible, then think they understand it, and then fall for it again when certain elements are changed.", 'The discussion of the Monty Hall problem with a million doors illustrates the extreme confidence in the need to switch doors, highlighting the counterintuitive nature of the problem and the importance of conditional thinking.', 'The insight that with a million doors, one would be extremely confident that the initial guess is wrong and that the remaining door has the car, demonstrating the counterintuitive nature of the problem and the need for conditional thinking.', 'The explanation of how the Monty Hall problem with a million doors is conceptually similar to the classic three-door problem, emphasizing the application of the one-half probability argument in both scenarios.']}], 'duration': 313.183, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1293470.jpg', 'highlights': ['Simple simulations show that two-thirds of the time one succeeds by switching, challenging intuition.', 'The Monty Hall problem with a million doors illustrates the extreme confidence in the need to switch doors.', 'The explanation of how the Monty Hall problem with a million doors is conceptually similar to the classic three-door problem.', 'The chapter emphasizes the utility of considering simple and extreme cases for complicated problems.', 'The insight that with a million doors, one would be extremely confident that the initial guess is wrong.']}, {'end': 2053.598, 'segs': [{'end': 1678.49, 'src': 'embed', 'start': 1655.356, 'weight': 0, 'content': [{'end': 1664.889, 'text': 'And at first that sounds wrong to most people, because it sounds like if person A is better than person B in every single category,', 'start': 1655.356, 'duration': 9.533}, {'end': 1669.575, 'text': "then when you aggregate those categories together it's not gonna somehow flip right?", 'start': 1664.889, 'duration': 4.686}, {'end': 1671.227, 'text': "Except that's wrong.", 'start': 1670.086, 'duration': 1.141}, {'end': 1678.49, 'text': "Simpson's Paradox says it can flip, that the sign of inequalities can flip when you aggregate data together.", 'start': 1671.227, 'duration': 7.263}], 'summary': "Simpson's paradox: inequalities can flip when aggregating data.", 'duration': 23.134, 'max_score': 1655.356, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1655356.jpg'}, {'end': 1725.01, 'src': 'embed', 'start': 1699.184, 'weight': 2, 'content': [{'end': 1705.785, 'text': "Okay so, I like to illustrate Simpson's Paradox through examples that I make up based on The Simpsons.", 'start': 1699.184, 'duration': 6.601}, {'end': 1717.088, 'text': "As I've been watching The Simpsons since I was a kid, and I like the show, and it helps me remember the example that it's Simpson's Paradox.", 'start': 1707.686, 'duration': 9.402}, {'end': 1720.269, 'text': "So I don't know how many of you watch The Simpsons, but it doesn't matter if you do.", 'start': 1717.228, 'duration': 3.041}, {'end': 1725.01, 'text': 'On The Simpsons, there are two doctors, Dr. Hibbert and Dr. Nick.', 'start': 1720.289, 'duration': 4.721}], 'summary': "Using the simpsons to illustrate simpson's paradox, with two doctors, dr. hibbert and dr. nick.", 'duration': 25.826, 'max_score': 1699.184, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1699184.jpg'}], 'start': 1607.194, 'title': "Simpson's paradox", 'summary': "Explores simpson's paradox, demonstrating how one doctor can have a higher success rate in every type of surgery, yet the other doctor has an overall higher success rate due to data aggregation, challenging common understanding of inequalities and aggregates. it also explains simpson's paradox using a hypothetical scenario involving dr. hibbert and dr. nick from the simpsons, illustrating how conditional and unconditional success rates can lead to paradoxical conclusions.", 'chapters': [{'end': 1698.181, 'start': 1607.194, 'title': "Understanding simpson's paradox", 'summary': "Explores simpson's paradox, demonstrating how it is possible for one doctor to have a higher success rate in every type of surgery, yet the other doctor has an overall higher success rate due to the aggregation of data, challenging the common understanding of inequalities and aggregates.", 'duration': 90.987, 'highlights': ["Simpson's Paradox explains how one doctor can have a higher success rate in every type of surgery, yet the other doctor has an overall higher success rate due to the aggregation of data, challenging the common understanding of inequalities and aggregates.", 'The paradox illustrates that the sign of inequalities can flip when data is aggregated, causing a seeming superiority in individual cases to reverse when combined.', 'It prompts a reevaluation of the way data is aggregated and interpreted, challenging traditional assumptions about aggregating and comparing data.']}, {'end': 2053.598, 'start': 1699.184, 'title': "Simpson's paradox: the simpsons example", 'summary': "Explains simpson's paradox using a hypothetical scenario involving dr. hibbert and dr. nick from the simpsons, illustrating how the conditional and unconditional success rates can lead to paradoxical conclusions.", 'duration': 354.414, 'highlights': ["The chapter illustrates Simpson's Paradox using the example of Dr. Hibbert and Dr. Nick from The Simpsons, highlighting the conditional and unconditional success rates for different types of surgeries, demonstrating how the aggregation of data can lead to paradoxical conclusions. The example of Dr. Hibbert and Dr. Nick from The Simpsons is used to demonstrate Simpson's Paradox, emphasizing the conditional and unconditional success rates for different types of surgeries, and how the aggregation of data can lead to paradoxical conclusions.", 'The transcript contains a hypothetical scenario involving Dr. Hibbert and Dr. Nick, where Dr. Nick appears to have a higher overall success rate despite performing poorly in specific surgeries, showcasing the paradoxical nature of aggregated data. The scenario involving Dr. Hibbert and Dr. Nick demonstrates the paradoxical nature of aggregated data, as Dr. Nick appears to have a higher overall success rate despite performing poorly in specific surgeries, emphasizing the need to consider conditional and unconditional success rates.', 'The chapter emphasizes the importance of considering conditional and unconditional success rates, as illustrated by the example of Dr. Hibbert and Dr. Nick, showcasing how the nature of surgeries and their success rates can lead to paradoxical interpretations. The importance of considering conditional and unconditional success rates is emphasized through the example of Dr. Hibbert and Dr. Nick, showcasing how the nature of surgeries and their success rates can lead to paradoxical interpretations, highlighting the complexities of aggregated data analysis.']}], 'duration': 446.404, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ1607194.jpg', 'highlights': ["Simpson's Paradox challenges common understanding of inequalities and aggregates.", 'The sign of inequalities can flip when data is aggregated, causing a seeming superiority in individual cases to reverse when combined.', "The chapter illustrates Simpson's Paradox using the example of Dr. Hibbert and Dr. Nick from The Simpsons, highlighting the conditional and unconditional success rates for different types of surgeries, demonstrating how the aggregation of data can lead to paradoxical conclusions."]}, {'end': 2940.219, 'segs': [{'end': 2106.478, 'src': 'embed', 'start': 2074.21, 'weight': 0, 'content': [{'end': 2082.195, 'text': 'How can it flip like that? Okay, so let me explain it a couple other ways and mention a couple other examples.', 'start': 2074.21, 'duration': 7.985}, {'end': 2089.92, 'text': "Another way to think of Simpson's Paradox, well, here's another example.", 'start': 2085.737, 'duration': 4.183}, {'end': 2102.016, 'text': "In baseball, it's possible to have two players where the first player has a higher batting average.", 'start': 2095.072, 'duration': 6.944}, {'end': 2106.478, 'text': 'A batting average is just what percentage of times they were at bat that they got a hit.', 'start': 2102.216, 'duration': 4.262}], 'summary': "Explaining simpson's paradox with a baseball example.", 'duration': 32.268, 'max_score': 2074.21, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ2074210.jpg'}, {'end': 2248.451, 'src': 'embed', 'start': 2200.182, 'weight': 1, 'content': [{'end': 2203.444, 'text': "But since that's not how we add fractions, it doesn't happen.", 'start': 2200.182, 'duration': 3.262}, {'end': 2207.547, 'text': "OK, there are a lot of other examples of Simpson's Paradox.", 'start': 2205.125, 'duration': 2.422}, {'end': 2212.03, 'text': 'If you just look at the Wikipedia entry and you can find as many as you want,', 'start': 2207.587, 'duration': 4.443}, {'end': 2219.314, 'text': 'examples that happen in real life and actually have policy implications and legal.', 'start': 2212.03, 'duration': 7.284}, {'end': 2222.456, 'text': "There are some interesting legal cases involving Simpson's Paradox.", 'start': 2219.654, 'duration': 2.802}, {'end': 2231.059, 'text': "Let me talk about how do we express Simpson's Paradox in terms of conditional probability.", 'start': 2225.155, 'duration': 5.904}, {'end': 2238.624, 'text': 'So just to kind of map this example into some events,', 'start': 2231.579, 'duration': 7.045}, {'end': 2248.451, 'text': "let's let A be the event that surgery suppose someone's gonna have surgery and let A be the event that the surgery is successful.", 'start': 2238.624, 'duration': 9.827}], 'summary': "Simpson's paradox has real-life examples, legal cases, and implications for policy and conditional probability.", 'duration': 48.269, 'max_score': 2200.182, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ2200182.jpg'}, {'end': 2493.825, 'src': 'embed', 'start': 2466.062, 'weight': 6, 'content': [{'end': 2472.245, 'text': "So that's Simpson's Paradox, and this is just kind of like the general setting of Simpson's Paradox.", 'start': 2466.062, 'duration': 6.183}, {'end': 2477.488, 'text': "So basically any example of Simpson's Paradox can be written in this form.", 'start': 2472.265, 'duration': 5.223}, {'end': 2485.263, 'text': "So I would take the definition of Simpson's paradox is whenever you have these inequalities, but it flips when you aggregate in this way.", 'start': 2478.141, 'duration': 7.122}, {'end': 2488.404, 'text': "That's a concrete example, that's just the generic setting.", 'start': 2485.323, 'duration': 3.081}, {'end': 2493.825, 'text': 'Okay, so you should try to think intuitively about why is this possible by thinking about examples.', 'start': 2489.004, 'duration': 4.821}], 'summary': "Simpson's paradox occurs when inequalities flip upon aggregation, demonstrated in various examples.", 'duration': 27.763, 'max_score': 2466.062, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ2466062.jpg'}, {'end': 2722.391, 'src': 'embed', 'start': 2688.873, 'weight': 3, 'content': [{'end': 2698.838, 'text': "Okay, so let me mention one or two more examples of Simpson's Paradox.", 'start': 2688.873, 'duration': 9.965}, {'end': 2707.966, 'text': "So here's another one that's a pretty famous one that involved a court case.", 'start': 2701.604, 'duration': 6.362}, {'end': 2722.391, 'text': 'So what happened was that there was a lawsuit against UC Berkeley claiming sex discrimination in admissions to their graduate programs.', 'start': 2708.767, 'duration': 13.624}], 'summary': "Simpson's paradox: uc berkeley faced sex discrimination lawsuit in admissions.", 'duration': 33.518, 'max_score': 2688.873, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ2688873.jpg'}, {'end': 2829.032, 'src': 'embed', 'start': 2795.287, 'weight': 7, 'content': [{'end': 2801.95, 'text': "And certain departments are harder to get into than others, and somehow those things led to a Simpson's Paradox occurring.", 'start': 2795.287, 'duration': 6.663}, {'end': 2807.093, 'text': "All right, one more example of Simpson's Paradox.", 'start': 2803.912, 'duration': 3.181}, {'end': 2808.374, 'text': 'This is actually the first one.', 'start': 2807.153, 'duration': 1.221}, {'end': 2815.918, 'text': 'I love paradoxes for a long time, and this was the first one I ever saw, and I still find it helpful to think about it.', 'start': 2809.014, 'duration': 6.904}, {'end': 2818.059, 'text': 'So we have two.', 'start': 2817.198, 'duration': 0.861}, {'end': 2829.032, 'text': "Let's see, how does it work? We have two jars like that with jelly beans, although if I were phrasing it now, I would use gummy bears.", 'start': 2819.71, 'duration': 9.322}], 'summary': "The transcript discusses simpson's paradox and gives examples with jelly beans and gummy bears.", 'duration': 33.745, 'max_score': 2795.287, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ2795287.jpg'}], 'start': 2053.638, 'title': "Simpson's paradox", 'summary': "Explains simpson's paradox, its applications in various fields, and demonstrates how aggregated data can lead to counterintuitive results using examples from baseball, court cases, and conditional probability, emphasizing the reversal of trends and implications of conditioning on certain variables.", 'chapters': [{'end': 2465.122, 'start': 2053.638, 'title': "Understanding simpson's paradox", 'summary': "Explains simpson's paradox and illustrates it with examples from different fields, such as baseball and conditional probability, showing how aggregated data can lead to counterintuitive results.", 'duration': 411.484, 'highlights': ["Simpson's Paradox in baseball Two players with higher batting averages for the first and second half of the season having a lower overall batting average, showcasing the paradoxical nature of aggregated data.", "Applying Simpson's Paradox to conditional probability Illustrating Simpson's Paradox using events of surgery success probability, revealing how the aggregation of data can lead to misleading conclusions if not properly conditioned.", "Explanation using fractions and aggregation Comparing the aggregation of successes and trials to adding fractions, demonstrating how the incorrect method of aggregation can lead to Simpson's Paradox.", "Implications of Simpson's Paradox in real-life examples Mentioning real-life examples and legal cases where Simpson's Paradox has policy and legal implications, showcasing its relevance and impact."]}, {'end': 2940.219, 'start': 2466.062, 'title': "Understanding simpson's paradox", 'summary': "Explains simpson's paradox, its general setting, mathematical equations, and provides examples including a court case involving uc berkeley's graduate programs and a scenario with jelly beans, highlighting how aggregation can lead to a reversal of trends and implications of conditioning on certain variables.", 'duration': 474.157, 'highlights': ['UC Berkeley lawsuit example - Highlighting the paradoxical nature of aggregating admission rates across all departments, which initially suggested discrimination against women, but when examined at the department level, there was no clear evidence of discrimination.', "Jelly bean scenario - Demonstrating through a concrete example how aggregating two better jars can lead to a higher percentage of a specific jelly bean, showcasing the counterintuitive nature of Simpson's Paradox.", "Explanation of mathematical equations - Detailed breakdown of the mathematical equations and conditional probabilities involved in Simpson's Paradox, highlighting the complexities and implications of conditioning on specific variables.", "General setting of Simpson's Paradox - Explaining the fundamental concept and generic setting of Simpson's Paradox, providing a clear understanding of its nature and applicability in various scenarios.", "Importance of considering examples and intuition - Emphasizing the significance of intuitive thinking and examples in understanding the possibility and implications of Simpson's Paradox, encouraging practical application for better comprehension."]}], 'duration': 886.581, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/fDcjhAKuhqQ/pics/fDcjhAKuhqQ2053638.jpg', 'highlights': ["Explains simpson's paradox using baseball example.", "Illustrates Simpson's Paradox using surgery success probability.", "Demonstrates implications of Simpson's Paradox in real-life examples.", 'UC Berkeley lawsuit example showcases paradoxical nature of aggregation.', "Demonstrates counterintuitive nature of Simpson's Paradox using jelly bean scenario.", "Provides detailed breakdown of mathematical equations in Simpson's Paradox.", "Explains the fundamental concept and generic setting of Simpson's Paradox.", "Emphasizes the significance of intuitive thinking and examples in understanding Simpson's Paradox."]}], 'highlights': ['The Monty Hall problem is a famous conditional probability problem that has been featured in various media.', 'The problem is known for deceiving almost everyone upon initial encounter.', 'The chapter aims to provide additional ways to think about the Monty Hall problem and approach it from more than one perspective.', "Monty Hall problem involves a game show scenario with three doors, where one door has a car and the other two have goats, and the contestant must choose a door without knowing what's behind it.", 'Monty always opens a door with a goat, and the player is given the option to switch to another unopened door.', 'The chapter discusses the Monty Hall problem, where Monty has the choice of which door to open with equal probabilities, leading to the conclusion that you should switch doors under these assumptions.', 'Switching yields a 2/3 probability of success, while sticking yields 1/3.', 'The abuse of the naive definition of probability is emphasized, questioning the assumption of equal likelihood.', 'Initial probabilities of 1/3, 1/3, 1/3 change after observing evidence, debunking misconceptions.', 'The relevance of Monty opening door two and the presence of a goat behind it is discussed.', 'The chapter suggests multiple approaches to understanding the problem, cautioning against incorrect reasoning.', 'The tree diagram is used to calculate conditional probabilities, demonstrating the advantage of switching doors.', 'The analysis concludes that two-thirds of the time, switching doors provides the correct answer.', 'The intuitive understanding that two-thirds of the time, switching doors results in success is explained.', "The law of total probability, LOTP, is preferred over Bayes' rule for solving the problem at hand.", 'In probability problems, wishing for specific information provides a hint as to what to condition on, such as wishing to know the location of the car in a given scenario.', 'The key step in using the law of total probability is deciding what to condition on, with the unique aspect of probability being the ability to use wishful thinking to determine the conditioning variable.', 'The unconditional and conditional probability of success in the Monty Hall problem using the switching strategy are both 2 thirds.', 'Mention of the controversy surrounding the Monty Hall problem. The transcript briefly discusses the controversy surrounding the Monty Hall problem, which began when Marilyn Vos Savant, who writes a column in Parade magazine, received a question about it.', 'Link to online applets for trying out the Monty Hall problem. There is a mention of the availability of applets online, including a link to a New York Times applet provided on the webpage for trying out the Monty Hall problem.', 'Simple simulations show that two-thirds of the time one succeeds by switching, challenging intuition.', 'The Monty Hall problem with a million doors illustrates the extreme confidence in the need to switch doors.', 'The explanation of how the Monty Hall problem with a million doors is conceptually similar to the classic three-door problem.', 'The chapter emphasizes the utility of considering simple and extreme cases for complicated problems.', 'The insight that with a million doors, one would be extremely confident that the initial guess is wrong.', "Simpson's Paradox challenges common understanding of inequalities and aggregates.", 'The sign of inequalities can flip when data is aggregated, causing a seeming superiority in individual cases to reverse when combined.', "The chapter illustrates Simpson's Paradox using the example of Dr. Hibbert and Dr. Nick from The Simpsons, highlighting the conditional and unconditional success rates for different types of surgeries, demonstrating how the aggregation of data can lead to paradoxical conclusions.", "Explains simpson's paradox using baseball example.", "Illustrates Simpson's Paradox using surgery success probability.", "Demonstrates implications of Simpson's Paradox in real-life examples.", 'UC Berkeley lawsuit example showcases paradoxical nature of aggregation.', "Demonstrates counterintuitive nature of Simpson's Paradox using jelly bean scenario.", "Provides detailed breakdown of mathematical equations in Simpson's Paradox.", "Explains the fundamental concept and generic setting of Simpson's Paradox.", "Emphasizes the significance of intuitive thinking and examples in understanding Simpson's Paradox."]}