you are a quality inspector for incoming parts to the factor

you are a quality inspector for incoming parts to the factory. Your company recieves connectors from two different suppliers. From suplier 1, the proability that a connector is faulty is .08. From supplier 2, the probability that a connector is faulty is .10. 40% of the connectors come from supplier 1 and 60% of the connectors come from supplier 2. You select a connector at random. Given that a connector is good. What is the probabiltiy that it came from suppplier 1?

Solution

Let

G = good
F = faulty

Thus,

P(1|G) = P(1) P(G|1) / P(G)

As

P(G) = P(1) P(G|1) + P(2) P(G|2) = 0.40*(1-0.08) + 0.60*(1-0.10)

P(G) = 0.908

Thus,

P(1|G) = P(1) P(G|1) / P(G) = 0.40*(1-0.08)/0.908

= 0.405286344 [ANSWER]