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Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:03,030 --> 00:00:05,190 Instructor: Welcome back everybody. 2 00:00:05,190 --> 00:00:08,160 Many scientific papers rely on conducting experiments 3 00:00:08,160 --> 00:00:09,780 or surveys. 4 00:00:09,780 --> 00:00:11,880 They often provide summarized statistics 5 00:00:11,880 --> 00:00:13,680 we use to analyze and interpret 6 00:00:13,680 --> 00:00:16,440 how certain factors affect one another. 7 00:00:16,440 --> 00:00:18,440 An example would illustrate this better. 8 00:00:19,350 --> 00:00:20,910 Imagine you conducted a survey 9 00:00:20,910 --> 00:00:23,730 where 100 men and women of all ages were asked 10 00:00:23,730 --> 00:00:25,560 if they eat meat. 11 00:00:25,560 --> 00:00:28,260 The results are summarized in the table on the screen. 12 00:00:29,220 --> 00:00:33,390 We see 15 of the 47 women that participated are vegetarian 13 00:00:33,390 --> 00:00:36,033 as are 29 out of the 53 men. 14 00:00:37,200 --> 00:00:40,530 Now, if A represents being vegetarian 15 00:00:40,530 --> 00:00:43,260 and B represents being a woman 16 00:00:43,260 --> 00:00:45,060 then P of A, 17 00:00:45,060 --> 00:00:46,260 given B 18 00:00:46,260 --> 00:00:47,730 and P of B, 19 00:00:47,730 --> 00:00:48,810 given A 20 00:00:48,810 --> 00:00:50,940 express different events. 21 00:00:50,940 --> 00:00:54,000 The former equals 15 over 47 22 00:00:54,000 --> 00:00:57,930 and represents the likelihood of a woman being vegetarian. 23 00:00:57,930 --> 00:01:01,140 While the latter equals 15 over 44 24 00:01:01,140 --> 00:01:05,640 and expresses the likelihood of a vegetarian being a woman. 25 00:01:05,640 --> 00:01:10,500 Since 15 over 44 is greater than 15 over 47, 26 00:01:10,500 --> 00:01:13,620 it is more likely for a vegetarian to be female 27 00:01:13,620 --> 00:01:15,543 than for of a woman not to eat meat. 28 00:01:16,770 --> 00:01:18,150 That's quite interesting 29 00:01:18,150 --> 00:01:20,580 and shows you that in probability theory 30 00:01:20,580 --> 00:01:22,293 things are never straightforward. 31 00:01:23,670 --> 00:01:25,590 Now that you understand the distinctions between 32 00:01:25,590 --> 00:01:28,470 the different conditional probabilities of two events, 33 00:01:28,470 --> 00:01:31,020 we can introduce an important concept, 34 00:01:31,020 --> 00:01:33,333 the law of total probability. 35 00:01:34,830 --> 00:01:36,030 Okay. 36 00:01:36,030 --> 00:01:40,110 Imagine A is the union of some finitely many events, 37 00:01:40,110 --> 00:01:43,053 B1, B2 and so on. 38 00:01:43,950 --> 00:01:46,530 This law dictates that the probability of A is 39 00:01:46,530 --> 00:01:49,290 the sum of all the conditional probabilities of A 40 00:01:49,290 --> 00:01:51,540 given some B multiplied 41 00:01:51,540 --> 00:01:54,093 by the probability of the associated B. 42 00:01:55,950 --> 00:01:57,120 To clear any confusion. 43 00:01:57,120 --> 00:01:59,790 Let us go back to the survey example. 44 00:01:59,790 --> 00:02:01,950 The probability of being vegetarian 45 00:02:01,950 --> 00:02:05,580 equals the sum of the probability of being a vegetarian 46 00:02:05,580 --> 00:02:07,260 given the person is male 47 00:02:07,260 --> 00:02:09,690 times the probability of being male 48 00:02:09,690 --> 00:02:12,150 and the probability of being a vegetarian 49 00:02:12,150 --> 00:02:13,920 given the person is female 50 00:02:13,920 --> 00:02:17,013 multiplied by the probability of being female. 51 00:02:18,270 --> 00:02:20,130 If we plug in values from the table, 52 00:02:20,130 --> 00:02:22,500 we get the probability of being vegetarian 53 00:02:22,500 --> 00:02:25,260 equals 29 over 53, 54 00:02:25,260 --> 00:02:28,170 times 53 over 100, 55 00:02:28,170 --> 00:02:30,930 plus 15 over 47, 56 00:02:30,930 --> 00:02:33,153 times 47 over 100. 57 00:02:34,560 --> 00:02:36,690 That's 44 over 100 58 00:02:36,690 --> 00:02:38,613 or 0.44. 59 00:02:39,540 --> 00:02:41,340 Therefore, according to the survey 60 00:02:41,340 --> 00:02:45,123 there is a 44% chance of someone being vegetarian. 61 00:02:46,110 --> 00:02:48,030 We can refer back to the table and confirm 62 00:02:48,030 --> 00:02:51,870 the probability of being vegetarian is indeed 0.44. 63 00:02:51,870 --> 00:02:53,913 So our answer checks out. 64 00:02:55,440 --> 00:02:56,370 Great. 65 00:02:56,370 --> 00:02:57,270 In the next video 66 00:02:57,270 --> 00:02:59,310 we are going to introduce the Additive Law 67 00:02:59,310 --> 00:03:01,560 and the multiplication rule. 68 00:03:01,560 --> 00:03:02,673 Thanks for watching. 4868

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