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Homework Solutions 02

# Homework Solutions 02 - (W4150 Intro to Probability and...

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Solutions to Homework #2 (W4150 ‘Intro to Probability and Statistics’, S04) Sec. 2.5. (8) Let A = {there is a defect in braking system} and B = {there is a defect in fueling system}. We are given that P(A) = .25, P(B) = .17 and P(A B) = .15. Then: (a) P(A B) = P(A) + P(B) - P(A B) = .25 + .17 - .15 = .27 (b) P (No defect) = 1 – P(A B) = 1 - .27 = .73 Sec. 2.5. (12) (a) The total number of books on the shelf is 9 there are N = C 9 3 = 84 ways to pick 3 books. Furthermore, there is just one way to pick a dictionary (so n 1 =1) and C 8 2 = 28 = n 2 ways to pick two other books out of remaining 8. Hence, by multiplicative rule n = n 1* n 2 and P(*) = n/N = 28/84 = 1/3 (b) By the same reasoning P(**) = C 5 2 *C 3 1 / C 9 3 = 5/14 Sec. 2.7. (1) (a) The probability that a convict who pushed dope, also committed armed robbery; (b) The probability that a convict who committed armed robbery, also pushed dope; (c) The probability that a convict who didn’t push dope, also didn’t commit armed robbery; Sec. 2.7. (2) We are interested in finding the probability P(S|A) = P(student is a senior, given that (s)he got A on final). Because we are choosing at random from those who got A, this leaves us

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