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prob.part14.29_30

# prob.part14.29_30 - 1.2 DISCRETE PROBABILITY DISTRIBUTIONS...

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1.2. DISCRETE PROBABILITY DISTRIBUTIONS 21 we see that 2 m (C) + 2 m (C) + m (C) = 1 , which implies that 5 m (C) = 1. Hence, m (A) = 2 5 , m (B) = 2 5 , m (C) = 1 5 . Let E be the event that either A or C wins. Then E = { A,C } , and P ( E ) = m (A) + m (C) = 2 5 + 1 5 = 3 5 . ± In many cases, events can be described in terms of other events through the use of the standard constructions of set theory. We will brieFy review the de±nitions of these constructions. The reader is referred to ²igure 1.7 for Venn diagrams which illustrate these constructions. Let A and B be two sets. Then the union of A and B is the set A B = { x | x A or x B } . The intersection of A and B is the set A B = { x | x A and x B } . The di³erence of A and B is the set A - B = { x | x A and x ±∈ B } . The set A is a subset of B , written A B , if every element of A is also an element of B . ²inally, the complement of A is the set ˜ A = { x | x Ω and x ±∈ A } . The reason that these constructions are important is that it is typically the

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prob.part14.29_30 - 1.2 DISCRETE PROBABILITY DISTRIBUTIONS...

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