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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
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Consider randomly selecting a single individual and having

Chapter 3, Problem 87E

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QUESTION:

Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by A? 1 =likes vehicle #1 A? 2 =likes vehicle #2 A? 3 =likes vehicle #3 Suppose that P(A1)= .55,P(A2) = .65,P(A3 )= .70,P(A1 ?A2) = .80, P(A2 ?A3) = .40, and P(A1 ?A2?A3)=.88. a.? ?What is the probability that the individual likes both vehicle #1 and vehicle #2? b.? ?Determine and interpretP(A2|A3) . c.? re A2 and A3 independent events? Answer in two different ways. d. ?If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles?

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QUESTION:

Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by A? 1 =likes vehicle #1 A? 2 =likes vehicle #2 A? 3 =likes vehicle #3 Suppose that P(A1)= .55,P(A2) = .65,P(A3 )= .70,P(A1 ?A2) = .80, P(A2 ?A3) = .40, and P(A1 ?A2?A3)=.88. a.? ?What is the probability that the individual likes both vehicle #1 and vehicle #2? b.? ?Determine and interpretP(A2|A3) . c.? re A2 and A3 independent events? Answer in two different ways. d. ?If you learn that the individual did not like vehicle #1, what now is the probability that he/she liked at least one of the other two vehicles?

ANSWER:

Solution: Step 1: Given an experiment that randomly selecting a single individual and having that person test drive 3 different vehicles. 3 events are defined by A1: likes vehicle #1 A2: likes vehicle #2 A3: likes vehicle # 3 Here it is also given that P(A1)=.55 P(A3)= .70 P(A2 A3) = .40 P(A2)= .65 P(A1 A2)=.80 P(A1 A2 A3)=.88

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