Bob is 70% sure that Helen should be promoted to a management position. In order to increase the probability of making the right decision, he sends her for a psychological test. The test isn’t perfect, but the company has records of the test results from people who’ve gone on to become either successful or unsuccessful managers in the past. P(pass|successful manager) = 0.95; P(pass|unsuccessful manager) = 0.1. Helen passes the test.
QUESTION: What is the probability of Helen becoming a successful manager?