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Problem 4: Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by A1 = likes vehicle #1, A2 = likes vehicle #2, A3 = likes vehicle #3. Suppose that P(A1) = 0.63, P(A2) = 0.58, P(A3) = 0.72, P(A1 U A2) = 0.83, P(A2 n A3) = 0.45, and P(A1 U A2 U A3) = = 0.90. a. What is the probability that the individual likes both vehicle #1 and vehicle #2? b. Are A2 and A3 independent events? Justify your answer. c. 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

Problem 4: Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by A1 = likes vehicle #1, A2 = likes vehicle #2, A3 = likes vehicle #3. Suppose that P(A1) = 0.63, P(A2) = 0.58, P(A3) = 0.72, P(A1 U A2) = 0.83, P(A2 n A3) = 0.45, and P(A1 U A2 U A3) = = 0.90. a. What is the probability that the individual likes both vehicle #1 and vehicle #2? b. Are A2 and A3 independent events? Justify your answer. c. 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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 4: Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by A1 = likes vehicle #1, A2 = likes vehicle #2, A3 = likes vehicle #3. Suppose that P(A1) = 0.63, P(A2) = 0.58, P(A3) = 0.72, P(A1 U A2) = 0.83, P(A2 n A3) = 0.45, and P(A1 U A2 U A3) = 0.90. a. What is the probability that the individual likes both vehicle #1 and vehicle #2? b. Are A2 and A3 independent events? Justify your answer. c. 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
Transcribed Image Text:Problem 4: Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, and A3 by A1 = likes vehicle #1, A2 = likes vehicle #2, A3 = likes vehicle #3. Suppose that P(A1) = 0.63, P(A2) = 0.58, P(A3) = 0.72, P(A1 U A2) = 0.83, P(A2 n A3) = 0.45, and P(A1 U A2 U A3) = 0.90. a. What is the probability that the individual likes both vehicle #1 and vehicle #2? b. Are A2 and A3 independent events? Justify your answer. c. 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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