Discrete Mathematics with Graph Theory (3rd Edition) 197

Discrete Mathematics with Graph Theory (3rd Edition) 197 -...

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Section 7.4 195 12. Here A n B = 0, so P(A n B) = o. So P(A I B) = 0 and P(B I A) = o. A and B are not independent because P(A)P(B) = ;4 (~~) while P(A n B) = o. A and B are mutually exclusive because A n B = 0. 13. [BB] Let A be the event "a 1 appears on the first die" and B the event "a 1 appears on the second die." A and B are not mutually exclusive because (1,1) belongs to A n B. However, P(A) = ~ = P(B) and P(A n B) = 3 1 6 = P(A)P(B), so A and B are independent. 14. A and B are independent and mutually exclusive if and only if An B = 0 and either P(A) = 0 or P(B) = O. To see this, note first that if these conditions hold, then A and B are certainly mutually exclusive and they are independent because P(A n B) = 0 = P(A)P(B). Conversely, if A and B are mutually exclusive, then A n B = 0, so P(A)P(B) = P(A n B) = 0, implying P(A) = 0 or P(B) = O. 15. (a) [BB] Here P(A) = ~, P(B) = ~, P(A n B) = ~. So P(A n B) =I- P(A)P(B). (b) [BB] Here
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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