Question

A manufacturer obtains​ clock-radios from three different​ subcontractors: ​10% from​ A, ​20% from​ B, and ​70% from C. The defective rates for these subcontractors are ​5%, ​4, and 1% respectively. If a defective​ clock-radio is returned by a​ customer, what is the probability that it came from subcontractor​ A?

Answer 1

25%

Explanation:

Use conditional probability:

P(A | defective) = P(A and defective) / P(defective)

P = (0.10 × 0.05) / (0.10 × 0.05 + 0.20 × 0.04 + 0.70 × 0.01)

P = 0.005 / 0.02

P = 0.25