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Tutor: Welcome back.
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Toward the end of the last section,
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we mentioned mutually exclusive sets without explaining
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what they are in detail.
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Well, mutually exclusive sets are sets which are not allowed
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to have any overlapping elements,
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graphically their circles never intersect.
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During the last couple of lectures,
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we introduced some important characteristics of such events.
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Mutually exclusive sets have the empty set
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as their intersection.
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Therefore, if the intersection of any number
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of sets is the empty set,
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then they must be mutually exclusive and vice versa.
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What about their union?
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If some sets are mutually exclusive,
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their union is simply the sum
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of all separate individual sets.
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Okay, earlier in the course we also mentioned
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how events have complements.
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In a similar way, sets have complements too.
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Such compliments consist of all values
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that are parts of the sample space,
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but not part of the set.
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For instance, imagine a set consisting
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of all the odd numbers, its complement would be the set
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of all even numbers.
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One thing to remember about complements
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is that they are always mutually exclusive,
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however not all mutually exclusive sets are complements.
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For instance, imagine A is the set of all even numbers
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and B is the set of all numbers ending in five.
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We know that any number ending with five is odd,
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so these two sets are definitely mutually exclusive.
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However, the complement of all even is all odd
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and not just the ones ending with five.
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Therefore, a number like 13 would be part of the compliment,
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but not the set B.
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After the short clarification
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we are ready to dive deeper into probability theory.
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In the next lecture, we are going to explain
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the differences between independent and dependent events.
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Thanks for watching.
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