A foreman for an injection-molding firm admits that on 13% 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 21%. if a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective?

Question

Karen Hanna

Mathematics

16 December, 07:50

A foreman for an injection-molding firm admits that on 13% 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 21%. if a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective?

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Jazmyn Shea · Answer 1

Percentage of admitting molding and forgetting to shut off = 13%

And not forget to shut off F' = 87%

Defective molding D = 21%

P (F & D) = 13% * 21% = 2.73%

P (F ' & D) = 87% * 4% = 3.48%

P (D) = sum of the both probabilities P (F & D) and P (F ' & D) = 6.21%