A family that owns two automobiles is selected at random. Suppose that the proba

Question

A family that owns two automobiles is selected at random. Suppose that the probability that the older car is green is 0.35, the probability that the newer car is green is 0.5, and the probability that both the older and the newer cars are green is 0.1. Round your answers to 4 decimal places.

Q7 A family that owns two automobiles is selected at random. Suppose that the probability that the older car is green is 0.35, the probability that the newer car is green is 0.5, and the probability that both the older and the newer cars are green is 0.1. Round your answers to 4 decimal places. a. Find the probability that at I 0.75 Computer's answer now shown above. You are correct. Your receipt no. is 163-1482 Previous Tries b. What is the probability that the newer car is green, given that the older car is green? Submit Answer Incorrect. Tries 1/5 Previous Tries c. What is the probability that the newer car is green, given that the older car is not green? Submit Answer Tries 0/5

Explanation / Answer

a. Let A denote the older car being green and B denote the newer car being green

Given P(A) = 0.35 P(B) = 0.5 P(A B) = 0.1

P(A U B) = P(A) + P(B) - P(A B)

= 0.35 + 0.5 - 0.1

= 0.75

b. P(B|A) = P(A B) / P(A)

= 0.1 / 0.35

= 0.2857

c. P(B|A') = P(A' B) / P(A')

= (P(B) - P(A B)) / (1 - P(A))

= (0.5 - 0.1) / (1 - 0.35)

= 0.4 / 0.65

= 0.6154

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