A foreman for an injection-molding firm admits that on 10% of his shifts, he for

Question

A foreman for an injection-molding firm admits that on 10% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 2% to 20%. Let F = forgets to shut off the injection machine and D = defective.

What proportion of the moldings from the early morning run is defective? Round to 2 decimals.

The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night? Round to 2 decimals.

Explanation / Answer

F = forgets to shut off the injection machine and

D = defective.

p(D) = P(D|F)P(F) + P(D|Fc)P(Fc) =

= 0.10 * 0.20 + 0.9 * 0.02 = 0.038

proportion of the moldings from the early morning run is defective=P(D) = 0.038

P(F|D) = 0.10*0.20/0.038 = 0.526315

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