Of the items manufactured by a certain process, 20% are defective.Of the defective items, 60% can be repaired.
a. Find the probability that a randomly chosen item is defective and cannot be repaired.
b. Find the probability that exactly 2 of 20 randomly chosen items are defective and cannot be repaired.
(a) Let D denote the event that the item is defective and let R denote the even that the item can be repaired. Then P(D) = 0.2 and P(R | D) = 0.6. Then 
= (1 - 0.6)(0.2) = 0.08.
(b) Let X be the number of items out of 20 that are defective and cannot be repaired. Then X~ Bin(20, 0.08).
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