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Unformatted text preview: Solution of Homework 9 : Discrete Probability Q1. Show that if A and B are independent events, then A and B are also independent events. Answer P ( A ) P ( B ) = parenleftBig 1- P ( A ) parenrightBigparenleftBig 1- P ( B ) parenrightBig = 1- P ( A )- P ( B ) + P ( A ) P ( B ) = 1- parenleftBig P ( A ) + P ( B )- P ( A ) P ( B ) parenrightBig = 1- parenleftBig P ( A ) + P ( B )- P ( A B ) parenrightBig A,B are independent = 1- P ( A B ) = P ( A B ) = P ( A B ) A, B are independent Note that this was only one way to prove it and there are several other alternatives. Q2. What is the probability of a five-card poker hand contains the ace of hearts? Answer Let E be the event that a five-card poker hand contains the ace of hearts. The number of elements in the event E is the number of ways to pick the other four cards, which is C (51 , 4). P ( E ) = | E | | S | = C (51 , 4) C (52 , 5) = 5 52 ....
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- Fall '08