Discrete Mathematics with Graph Theory (3rd Edition) 193

Discrete Mathematics with Graph Theory (3rd Edition) 193 -...

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Section 7.3 191 13 [BB] (a) (~) G) = -2. · C;) 44 (d) Let A be "majority of Americans" and B be "exactly four Canadians." From (a) and (b), we know P( A) = ~ and P( B) = ~~. Since A n B = 0, A and B are mutually exclusive, so the answer is P(A U B) = ~ + 14 = ~4' (d) Let A be "exactly three Americans" and B be "at most three Canadians." From (a) and (c), we know P(A) = ~~ and P(B) = i~~. The event "three Americans and two Canadians" is A n B, but this is just A. Thus U = ~~ + i~~ - ~~ = i~~. 15. [BB] (a) i~ (b) 1~ (c) i (d) 1~ (e) ~ 16. (a) ~gg (b) 2 3 l o (c) lo~ 17. Let A be "divisible by 3," B be "divisible by 5," and C be "divisible by 7." We want U B U C) - n B n C) = P(A) + + P(C) - n - n C) - P(B n C) 1666 1000 714 333 238 142 2667 = 5000 + + 5000 - = 5000' 18. (a) Using Exercise 15(a) of Section 6.1, we obtain 1~~~gO = ~6g~. L 10,000 J (b) This means divisible by 3(5) (7) (11) = 1155, so the answer is 1~1~~0
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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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