(b) A foreman for an inj ing firm admits that on 11% of his shifts, he forgets t

Question

(b) A foreman for an inj ing firm admits that on 11% 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 4% to 23%. What is the probability the plant manager randomly selects a molding from the early morning run and discovers it is defective? i) If the plant manager finds a defective molding, what is the probability that ihn3FC2Ens an ikrgyest in shut off thoiWal:/ilitr tho p,101E nigghit?

Explanation / Answer

i) Using total probability,
P(Shut off) = 0.89, P(Not shut off) = 0.11
P(Defective | shut off) = 0.04, P(Defective | not shut off) = 0.23

P(Defective) = P(Defective | Shut off) * P(Shut off) + P(Defective | not shut off) * P(not shut off)
= 0.04*0.89 + 0.23*0.11 = 0.0609

ii) P(Defective | Not shut off) = P(Defective and Not shut off) / P(Not shut off)
P(Defective and Not shut off) = 0.23 * 0.11 = 0.0253

P(Not shut off | Defective) = P(Defective and Not shut off)/P(Defective) = 0.0253/0.0609 = 0.4154

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