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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 --> 00:00:04,800 Instructor: Welcome back everybody. 2 00:00:04,800 --> 00:00:06,567 So far we've only talked about events 3 00:00:06,567 --> 00:00:08,400 and the theoretical probability 4 00:00:08,400 --> 00:00:12,360 of which remains unaffected by other events. 5 00:00:12,360 --> 00:00:15,450 We call these independent, and the simplest example 6 00:00:15,450 --> 00:00:16,623 is flipping a coin. 7 00:00:17,520 --> 00:00:20,160 You always have a 50% chance of getting tails 8 00:00:20,160 --> 00:00:23,223 regardless of the result obtained with the previous throw. 9 00:00:24,780 --> 00:00:27,990 In addition, we can have dependent events. 10 00:00:27,990 --> 00:00:30,423 Their probabilities vary as conditions change. 11 00:00:31,350 --> 00:00:33,090 For instance, take the probability 12 00:00:33,090 --> 00:00:34,743 of drawing the queen of spades. 13 00:00:35,610 --> 00:00:38,970 Normally the answer is 1 over 52 14 00:00:38,970 --> 00:00:41,490 since we have exactly one favorable outcome 15 00:00:41,490 --> 00:00:43,953 and 52 elements in the sample space. 16 00:00:45,390 --> 00:00:49,410 Now, imagine we know that the card we drew was a spade. 17 00:00:49,410 --> 00:00:52,620 Our chances of getting the queen of spades suddenly go up 18 00:00:52,620 --> 00:00:54,420 since the new sample space contains 19 00:00:54,420 --> 00:00:57,660 the 13 cards from the suit only. 20 00:00:57,660 --> 00:01:01,263 Therefore, the probability becomes 1 over 13. 21 00:01:02,820 --> 00:01:05,850 Okay, now imagine a different scenario. 22 00:01:05,850 --> 00:01:09,330 Instead of a spade, we know our card is a queen 23 00:01:09,330 --> 00:01:13,050 so the sample space only consists of four cards. 24 00:01:13,050 --> 00:01:14,580 Therefore, the probability of drawing 25 00:01:14,580 --> 00:01:18,243 the queen of spades becomes 1 over 4. 26 00:01:19,950 --> 00:01:22,830 With this example, you could clearly see how the probability 27 00:01:22,830 --> 00:01:26,760 of an event changes depending on the information we have. 28 00:01:26,760 --> 00:01:29,220 This is a very important insight relating 29 00:01:29,220 --> 00:01:30,333 to this whole section. 30 00:01:31,770 --> 00:01:35,163 Okay, before we move on, let's introduce some new notation. 31 00:01:36,480 --> 00:01:40,443 As usual, suppose we have two events, A and B, 32 00:01:41,280 --> 00:01:44,310 to express the probability of getting A, 33 00:01:44,310 --> 00:01:47,550 if we are given that B has occurred. 34 00:01:47,550 --> 00:01:50,247 We use the following notation, P(A|B). 35 00:01:56,160 --> 00:01:59,793 We read this as P of A given B. 36 00:02:01,200 --> 00:02:03,000 Going back to our card example, 37 00:02:03,000 --> 00:02:05,610 event A is drawing the queen of spades 38 00:02:05,610 --> 00:02:08,430 and event B is drawing a spade. 39 00:02:08,430 --> 00:02:12,420 Therefore, P of A given B would represent 40 00:02:12,420 --> 00:02:15,630 the probability of drawing the queen of spades, 41 00:02:15,630 --> 00:02:17,883 if we know the card is a spade. 42 00:02:18,990 --> 00:02:20,910 We already calculated this earlier, 43 00:02:20,910 --> 00:02:25,203 so P of A given B equals 1 over 13. 44 00:02:26,070 --> 00:02:30,120 Similarly, if event C represents getting a queen 45 00:02:30,120 --> 00:02:33,870 then P of A given C expresses the likelihood 46 00:02:33,870 --> 00:02:38,250 of getting the queen of spades, assuming we drew a queen. 47 00:02:38,250 --> 00:02:43,070 Thus, P of A given C equals 1 over 4. 48 00:02:44,820 --> 00:02:47,430 Perfect, we call this probability 49 00:02:47,430 --> 00:02:49,800 the conditional probability, and we use it 50 00:02:49,800 --> 00:02:52,683 to distinguish dependent from independent events. 51 00:02:53,580 --> 00:02:55,620 In the next lecture, we are going to show you 52 00:02:55,620 --> 00:02:59,520 how to compute it and interpret conditional probabilities. 53 00:02:59,520 --> 00:03:00,633 Thanks for watching. 4226

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