SOLUTION: of all the people applying for a certain job, 80% are qualified and 20% are not. The personnel claims that she approves qualified people 80% of the time; she approves unqualified p

Question 354931: of all the people applying for a certain job, 80% are qualified and 20% are not. The personnel claims that she approves qualified people 80% of the time; she approves unqualified people 80% of the time. find the probability that a person is not qualified if he or she was not approved by the manager.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Probability that she approves qualified = 0.80*0.80 = 0.64
probability that she doesn't approve qualified = 0.80*0.20 = 0.16
probability that she approves unqualified = 0.80*0.20 = 0.16
probability that she doesn't approve unqualified = 0.20*0.20 = 0.04
Then by the formula for conditional probability,
P(unqualified|not approved) = P(unqualified and not approved)/P(not approved)
= 0.04/(0.16+0.04) = 0.04/0.20 = 0.20.
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