Apply Bayes’s rule to find the probability that Hahn Engineering will win the bid. If they do, what is the probability that S&A did bid on it?

Hahn Engineering is planning on bidding on a job and often competes against a major competitor, Sweigart and Associates (S&A), as well as other firms. Historically, S&A has bid for the same jobs 80% of the time. If S&A bids on a job, the probability that Hahn Engineering will win it is 0.30. If S&A does not bid on a job, the probability that Hahn will win the bid is 0.60. Apply Bayes’s rule to find the probability that Hahn Engineering will win the bid. If they do, what is the probability that S&A did bid on it?

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