Question

A manufacturing firm produces pipes in two plants I and II with daily production 1,500 and 2,000 pipes respectively. The fraction of defective pipes produced by Plants I and II are 0.006 and 0.008 respectively. If a pipe selected at random from the days production is found to be defective, what is the probability that it has come from plant I, Plant II ?

Answer 1

P(production from plant I) $= \frac{1500}{3500} = 0.43$

P(production plant II) $= \frac{2000}{3500} = 0.57$

P(defective) $= 0.006 \times 0.43 + 0.008 \times 0.57 = 0.00714$

P(produced from plant I | defective) = P(defective | produced from plant I) $\times$ P(produced from pant I)/P(defective)

$= \frac{0.006 \times 0.43}{0.00714} = 0.3613$

P(produced from plant II | defective) = P(defective | produced from plant II) $\times$ P(produced from pant II)/P(defective)

$= \frac{0.008 \times 0.57}{0.00714} = 0.6387$