Of all the people applying for a certain job 60 are qualifie

Of all the people applying for a certain job, 60% are qualified and 40% are not. The personnel manager claims that she approves qualified people 75% of the time; she approves unqualified people 20% of the time. Find the probability that a person is not qualified if he or she was approved by the manager.

Solution

Probability that she approves qualified = 0.60*0.60 = 0.36

probability that she doesn\'t approve qualified = 0.60*0.40 = 0.24

probability that she approves unqualified = 0.60*0.40 = 0.24

probability that she doesn\'t approve unqualified = 0.40*0.40 = 0.16

Then by the formula for conditional probability,

P(unqualified|not approved) = P(unqualified and not approved)/P(not approved)

= 0.16/(0.24+0.16)

= 0.16/0.4

= 0.4