Of all the people applying for a certain job, $89\%$ are qualified. The personnel manager claims that she approves qualified people $61\%$ of the time and she approves an unqualified person $12\%$ of the time.
Find the probability that a randomly chosen applicant who was approved by the manager is qualified. Round your answer to the nearest tenth of a percent.
I tried it many times but I always failed. I do not know how to solve this I need help.
Best Answer
Let $Q$ mean 'applicant is qualified', $Q'$ 'applicant is not qualified' and $A$ 'approved'. We are given
$$P(Q) = 0.89, P(A|Q) = 0.61, P(A| Q') = 0.12$$
What have you written down for $P(Q|A)$?