Question

5) A consulting firm rent cars from three agencies: 30% from agency A, 20% from agency B and 50% from agency C. 15% of the cars from agency A, 10% of the cars from agency B and 6% of the cars from agency C. If a car rented by the firm has bad tires, find the probability that it came from: a) agency C b) agency A

Answer 1

If a car rented by the firm has bad tires, then the probability that it came from: a) agency C is:

$P(A|B) = \frac{0.5×0.06}{0.3×0.15 + 0.2×0.1 + 0.5×0.06} = \frac{0.03} {0.095} = 0.32.$

b) agency A is:

$P(A|B) = = \frac{0.3×0.15} {0.095} = 0.47.$