STAT 1000 Lecture Notes - Lecture 23: Sample Space, Venn Diagram, Empty Set
4 Dec 2017
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We can see that there are only two events that are in both a and b. S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45 , 46, 51, 52, 53, 54 , 55, 56, 61, 62, 63, 64, 65, 66} The probability of the union of two events can be calculated as. We can see that if we add the events a and b, then we have included the probability of. We could have used this rule to calculate the probability in the previous example: Two events are mutually exclusive (or disjoint) if they have no outcomes in common: Where is the empty set, a set containing no outcomes, i. e p( It follows that two events are mutually exclusive if and only if p(a and b) = 0. We have seen that p(a b) = p(a)+p(b) p(a b).
