solution05 - = P B ∩ C = 5 16 and P A P B = P A P C = P B...

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Solution 05 Section 4.1: 2. (a)1/2; (b)1/4; (c)1/2; (d)0; (e)1/2. 4. (a)1/2; (b)4/13; (c)1/13. 7. (a) We have P ( A B ) = P ( A C ) = P ( B C ) = 1 4 , P ( A ) P ( B ) = P ( A ) P ( C ) = P ( B ) P ( C ) = 1 4 , P ( A B C ) = 1 4 = P ( A ) P ( B ) P ( C ) = 1 8 . (b) We have P ( A C ) = P ( A ) P ( C ) = 1 4 , so C and A are independent, P ( C B ) = P ( B ) P ( C ) = 1 4 , so C and B are independent, P ( C ( A B )) = 1 4 = P ( C ) P ( A B ) = 1 8 , so C and A B are not independent. 8. We have P ( A B C ) = P ( { a } ) = 1 8 , and P ( A ) = P ( B ) = P ( C ) = 1 2 . Thus while P ( A B C ) = P ( A ) P ( B ) P ( C ) = 1 8 , we have P ( A B ) = P
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Unformatted text preview: ) = P ( B ∩ C ) = 5 16 , and P ( A ) P ( B ) = P ( A ) P ( C ) = P ( B ) P ( C ) = 1 4 . Therefore no two of these events are independent. 32. (a) pq ; (b) 1-(1-p )(1-q ); (c) .958 39. (a) 1/9; (b) 1/4; (c) No; (d) p z = ±-2-1 0 1 2 4 1 6 1 6 1 6 1 6 1 6 1 6 ² 1...
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