Prob.4 Customers who purchase a certain car can order an engine in any of three

Question

Prob.4 Customers who purchase a certain car can order an engine in any of three sizes. Of all cars sold, 45% have small-size engines, 35% have medium-size, and 20% have large-size engines. Of the cars with small size engines, 10% fail emission test within two years of purchase, while 12% of those with medium size and 15% of large size engine fail. (a) What is the probability that a randomly chosen car will fail emission test within two years? (b) A record for failed emission test is chosen at random. What is the probability that it is for a car with large size engine?

Explanation / Answer

a) P(fail emission)=P(small size and fail emission)+P(medium size and fail emission)+P(large size and fail emission)=0.45*0.1+0.35*0.12+0.2*0.15=0.117

b)

P(large size engine|fail emission)=P(large size and fail emission)/P(fail emission)

=0.2*0.15/0.117=0.25641

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