3-47. ACE Metal Products Corp. produces steel pins of a specific diameter. It uses three machines (denoted as A, B, and C) in the initial grinding phase of production. Machines A, B, and C have a history of producing 3%, 1%, and 2.5% defective pins, respectively. Machine A produces 45% of total production and machines B and C contribute 35% and 20%, respectively, to total production. If a pin is randomly chosen from the total amount produced for a given grinding phase production run, what is the probability that it was produced by machine A, given that the pin was found to conform to specifications?