Question

A consulting firm rents taxis from three agencies , 20% from agency A, 20% from agency B and 60% from agency C. if 10% of the taxis from A, 12 % of the taxis from B, and 4% of the taxis from C have bad tires.

a) What is the probability that the firm will get a taxi with bad tires?

b) What is the probability that a taxi with bad tires rented by the firm came from agency A?

Answer 1

a) The probability that the firm will get a taxi with bad tires is:

$P = 0.1×0.2 + 0.12×0.2 + 0.04×0.6 = 0.068$ or 6.8%.

b) The probability that a taxi with bad tires rented by the firm came from agency A using the formula for conditional probability is:

$P = 0.1×0.2/0.068 = 0.294$ or 29.4%.