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. The members of the consulting firm rent cars from three rental agencies: 60 pe

ID: 3043439 • Letter: #

Question

. The members of the consulting firm rent cars from three rental agencies: 60 percent from agency 1, 30 percent from agency 2, and 10 percent from agency 3. If9 percent of the cars from agency I need a tune-up, 20 percent of the cars from agency 2 need a tune-up, and 6 percent of the cars from agency 3 need a tune-up, i What is the probability that a rental car delivered to the firm will need a tune-up? What is the probability that a rental car delivered to the firm will NOT need a tune-up? ii. ii. If the rental car delivered to the consulting firm needs a tune-up, what is the probability that it comes from rental agency 1?

Explanation / Answer

Assume that we have 1000 cars.

Cars rented by agency 1 = 600

Cars rented by agency 2 = 300

Cars rented by agency 3 = 100

Cars from agency 1 that need a tune up = 54

Cars from agency 2 that need a tune up = 60

Cars from agency 3 that need a tune up = 6

(i)

Probability that the rental car will need a tune-up = (54+60+6)/1000 = 0.120

(ii)

Probability that the rental car will not need a tune-up = 1-0.120 = 0.880

(iii)

Probability that car is from agency 1 provided it needs a tune up = 54/(54+60+6) = 0.45

Hope this helps !