Question

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 10​% of the time. Find the probability that a person is qualified if he or she was not approved by the manager.

Answer 1

P(qualified) = 0.6

P(not qualified) = 0.4

P(she approves | qualified) = 0.75

P(she approves | unqualified) = 0.1

P(she approves) = P(she approves | qualified) * P(qualified) + P(she approves | unqualified) * P(unqualified)

                           = 0.75 * 0.6 + 0.1 * 0.4

                           = 0.49

P(not approved by manager) = 1 - P(she approves) = 1 - 0.49 = 0.51

P(she does not approve | qualified) = 1 - P(she approves | qualified) = 1 - 0.75 = 0.25

P(qualified | not approved by manager) = P(she does not approve | qualified) * P(qualified) / P(not approved by manager)

                                                               = 0.25 * 0.6 / 0.51

                                                               = 0.2941