Finite Chapter 7.3

Finite Chapter 7.3 - Math 120 SP08 SBrodnick 7.3:...

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Math 120 SP08 SBrodnick 1 1 7.3 : Properties of Probability Distributions 2 7.3: Properties of Probability Distributions * For any events A and B, P(AUB) = P(A) + P(B) – P(A B) * Recall: if A and B are mutually exclusive , A B = Ø, so P(A B) = 0 formula is just P(AUB) = P(A) + P(B) * Same idea for 3 mutually exclusive events, A, B, and C : P(AUBUC) = P(A) + P(B) + P(C) * If A, B, and C are not mutually exclusive… P(AUBUC) = P(A) + P(B) + P(C) – P(A B) – P(A C) – P(B C) + P(A B C) 3 Examples : 1. P(A) = 0.5, P(B) = 0.7, P(A B) = 0.3. P(AUB)? 2.A and B are mutually exclusive, P(B) = 0.62, P(AUB) = 0.77. P(A)? 3.P(AUB) = 0.79, P(B) = 0.56, P(A B) = 0.14. P(A)? 4.P(A) = 0.64, P(B) = 0.5, P(C) = 0.56, P(A B) = 0.25, P(A C) = 0.35, P(B C) = 0.15, and P(AUBUC) = 1. P(A B C)? 7.3: Properties of Probability Distributions 4 * A few properties …(sample space S, event A) 1. P(S) = 1 3. P(A’) = 1 – P(A) (i.e., P(A’) + P(A) = 1)
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