<s>[INST] There are 40 faculty candidates, and 20 of them are women. Event W = "Choosing a woman" and event M = "Choosing a man." The probability of event W occurring, P(W), is 20/40. If a decision to choose a woman is made, it will result in the success of the plan. We consider event W as a success in this plan. If event W occurs, we have a probability of 0.33 of choosing a woman who is a Ph.D. holder, P(W and PhD) = 0.33P(W). If the chosen woman is a Ph.D. holder, we have a 75% probability of the woman accepting the job. Let's define the probability of the woman accepting the job as P(A). If the woman accepts the job, the success of the plan will be 100%, i.e., P(S)|A = 1.[/INST]