Question

A certain firm has plants A, B and C producing, respectively, 35%, 15% and 50%, of the total out. The

probabilities of a non-defective product are, respectively, 0.75,0.95 and0.85. If a consumer receives a

defective product, what is the probability that it came from plant C.

Answer 1

By Bayes formula and the Law of total probability:

$P=\frac{0.5\cdot(1-0.85)}{0.35\cdot(1-0.75)+0.15\cdot(1-0.95)+0.5\cdot(1-0.85)}\approx0.44$