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Unformatted text preview: Answers to some exercises in chapter 3 and 4 (STAT 515, Fall 2011) 3.66. a. Because A and B are mutually exclusive, P ( A B ) = P ( A ) + P ( B ) = 0 . 85 . b. By the definition of mutually exclusive events, P ( A B ) = 0 . c. P ( A | B ) = P ( A B ) /P ( B ) = 0 , since the numerator is zero from part b . d. Because B and C are mutually exclusive, P ( B C ) = P ( B ) + P ( C ) = 0 . 70 . 3.70. a. Because the Venn diagram shows that P ( A C ) = P ( B C ) = 0 , so A and C are mutually exclusive, also B and C are mutually exclusive. b. According to part a , we know the following two pairs, ( A,C ) and ( B,C ) , are not inde- pendent. Note that mutually exclusive events cannot be independent events. Next check if A and B are independent. Note that P ( A B ) = P (3) = 0 . 3. Because P ( A ) = P (1) + P (2) + P (3) = 0 . 2 + 0 . 05 + 0 . 3 = 0 . 55 , and P ( B ) = P (3) + P (4) = . 3 + 0 . 1 = 0 . 4, therefore P ( A B ) 6 = P ( A ) P ( B ) . This implies that...
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This note was uploaded on 02/21/2012 for the course STAT 515 taught by Professor Zhao during the Fall '10 term at South Carolina.
- Fall '10
- Mutually Exclusive