Question

A foreman for an injection-molding firm admits that on 52% 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 25%. If a molding is randomly selected from the early morning run of a random day, what is the probability that it is defective

Answer 1

The probability that it is defective= 0.1396

Explanation:

Let D be the event of being Defective. When he forgets to shut off the machine 52% of the time the

P (D) = 0.25 * 0.52= 0.13

When he does not forget of shut off the injection machine ( 1- 0.52= 0.48) 48 % of the time the

P (D) = 0.02*0.48= 0.0096

Total Probability of Defect = Probability of Defect When forgetting + Probability of Defect when not forgetting

Total Probability of Defect = 0.13+ 0.0096= 0.1396