All language subtitles for 005 Mutually Exclusive Sets_en

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Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:03,150 --> 00:00:04,680 Tutor: Welcome back. 2 00:00:04,680 --> 00:00:05,820 Toward the end of the last section, 3 00:00:05,820 --> 00:00:08,520 we mentioned mutually exclusive sets without explaining 4 00:00:08,520 --> 00:00:10,560 what they are in detail. 5 00:00:10,560 --> 00:00:14,310 Well, mutually exclusive sets are sets which are not allowed 6 00:00:14,310 --> 00:00:16,920 to have any overlapping elements, 7 00:00:16,920 --> 00:00:20,223 graphically their circles never intersect. 8 00:00:21,420 --> 00:00:22,800 During the last couple of lectures, 9 00:00:22,800 --> 00:00:25,863 we introduced some important characteristics of such events. 10 00:00:27,180 --> 00:00:29,730 Mutually exclusive sets have the empty set 11 00:00:29,730 --> 00:00:31,800 as their intersection. 12 00:00:31,800 --> 00:00:34,320 Therefore, if the intersection of any number 13 00:00:34,320 --> 00:00:36,810 of sets is the empty set, 14 00:00:36,810 --> 00:00:40,473 then they must be mutually exclusive and vice versa. 15 00:00:41,700 --> 00:00:42,850 What about their union? 16 00:00:43,740 --> 00:00:45,930 If some sets are mutually exclusive, 17 00:00:45,930 --> 00:00:47,670 their union is simply the sum 18 00:00:47,670 --> 00:00:49,923 of all separate individual sets. 19 00:00:51,750 --> 00:00:54,660 Okay, earlier in the course we also mentioned 20 00:00:54,660 --> 00:00:57,210 how events have complements. 21 00:00:57,210 --> 00:01:00,630 In a similar way, sets have complements too. 22 00:01:00,630 --> 00:01:03,030 Such compliments consist of all values 23 00:01:03,030 --> 00:01:05,040 that are parts of the sample space, 24 00:01:05,040 --> 00:01:06,900 but not part of the set. 25 00:01:06,900 --> 00:01:09,270 For instance, imagine a set consisting 26 00:01:09,270 --> 00:01:12,990 of all the odd numbers, its complement would be the set 27 00:01:12,990 --> 00:01:14,793 of all even numbers. 28 00:01:16,830 --> 00:01:18,780 One thing to remember about complements 29 00:01:18,780 --> 00:01:21,900 is that they are always mutually exclusive, 30 00:01:21,900 --> 00:01:25,743 however not all mutually exclusive sets are complements. 31 00:01:26,730 --> 00:01:30,960 For instance, imagine A is the set of all even numbers 32 00:01:30,960 --> 00:01:34,203 and B is the set of all numbers ending in five. 33 00:01:35,070 --> 00:01:38,400 We know that any number ending with five is odd, 34 00:01:38,400 --> 00:01:42,060 so these two sets are definitely mutually exclusive. 35 00:01:42,060 --> 00:01:47,060 However, the complement of all even is all odd 36 00:01:47,130 --> 00:01:49,980 and not just the ones ending with five. 37 00:01:49,980 --> 00:01:54,030 Therefore, a number like 13 would be part of the compliment, 38 00:01:54,030 --> 00:01:55,443 but not the set B. 39 00:01:56,580 --> 00:01:58,050 After the short clarification 40 00:01:58,050 --> 00:02:00,813 we are ready to dive deeper into probability theory. 41 00:02:01,650 --> 00:02:03,720 In the next lecture, we are going to explain 42 00:02:03,720 --> 00:02:07,680 the differences between independent and dependent events. 43 00:02:07,680 --> 00:02:08,763 Thanks for watching. 3368

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