04 STAT HWB a

# 04 STAT HWB a - Dr V.R Bencivenga Economics 329 PRACTICE...

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Dr. V.R. Bencivenga Economics 329 PRACTICE HOMEWORK #4B: ANSWERS 1. P(detected by #1 detected by #2) = P(detected by #1) + P(detected by #2) P(detected by #1 detected by #2) = .85 + .85 .80 = .90 2.a. B = rented a car for business reasons C = rented a car for personal reasons P(B) = .54 P(C) = .51 P(B C) = .72 P(B C) = P(B) + P(C) P(B C) = .54 + .51 .72 = .33 b. B and C are independent iff P(B C) = P(B)P(C). Since .33 (.54)(.51) = .2754, B and C are dependent. c. P(did not rent a car) = ) C B ( P 28 . 72 . 1 ) C B ( P 1 ) C B ( P d. P(rented a car for business reasons only) = ) C B ( P = P(B) P(B C) = .54 .33 = .21 C B B C B C C B B C 3.a. I = correct intelligence P(I) = .90 T = troops and helicopters moved to staging area P(T) = .80 B = battleships in position P(B) = .70 S = troops delivered to secret position P(S | T) = .75 M = enough missiles get through P(M | B) = .95 The basic outcomes are enumerated on the next page.

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M e 1 S not M e 2 not I T B M e 3 not S not M e 4 not I not T B e 5 not I not T not B e 6 not I T not B e 7 M e 8 S not M e 9 I T B M e 10 not S not M e 11 I not T B e 12 I not T not B e 13 I T not B e 14 There are 14 basic outcomes, and S = {e 1 , , e 14 } b. P(retaliatory strike succeeds) = P(M S B T I) = P(I)P(S T)P(M B) This assumes independence across I, S T, and M B. Then P(I)P(S T)P(M B) = P(I)P(S | T)P(T)P(M | B)P(B) = (.95)(.75)(.70)(.80)(.90) = .3591 c. There are 2 4 = 16 basic outcomes if the characteristic of each strike is whether or not it succeeds . In 4 ! ) 3 4 ( ! 3 ! 4 C 3 4 of them, three of the strikes succeed, and one fails. The probability of any one of these four basic outcomes is (.3591) 3 (1 .3591) 1 = .0297. Therefore, the probability of three successful strikes and one failed strike is 4(.0297) = .1188.
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04 STAT HWB a - Dr V.R Bencivenga Economics 329 PRACTICE...

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