SOLUTION: 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

Question 1184914: 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 from 2%to 20% that a
defective molding will be produced during the early morning run. What proportion of moldings from the early morning run is defective
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
without the overheating, the probability of a defective molding is 2%.

if the probability holds true, then 2% of the moldings are expected to be deficient on the normal runs.

on 10% of the runs, the machine is allowed to overheat, causing the probability of a defective molding to be 20%, rather an 2%.

if the probability holds true, then 20% of the moldings are expected to be deficient on those runs where the machines are allowed to overheat.

what i get rom this is:

the overall probability of defective moldings appears to be 90% at 2% and 10% at 20% = .9 * 2% + .10 * 20% = 3.8%.

assume 1000 shifts.
90% are at 2% and 10% are at 20%.
900 shifts are at 2% and 100 shifts are at 20%.
.02 * 900 = 18 defectives in the normal runs.
.20 * 100 = 20 defectives in the overheated runs.
total defectives = 38.
38 / 100 3.8%.

i think this is how you would look at this.
give it a shot.
see how you do.

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