Question by Beer and Loathing: A foreman for an injection-molding firm admits that on 39% of his shifts, he forgets to shut off the machine?
A foreman for an injection-molding firm admits that on 39% 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 5% to 15%. 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?

Best answer:

Answer by M3
F = forgets to shut off
D = defective molding produced

P[F & D] = 39% * 15% = 5.85%
P[F’ & D] = 61% * 5% = 3.05%
P[D] = sum of the above = 8.90%

P[F | D] = P[F & D] / P[D]
= 5.85/8.90
= .657 or 65.7%
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