Solving problem N3814 Bayesian probability theory

Solving problem N3814 Bayesian probability theory

3814. The worker serves three machines on which the same parts are processed. The probability of rejection for the first machine is 0.02, for the second - 0.03, for the third - 0.04. The parts to be processed are folded in one box. The productivity of the first machine is three times more than the second, and the third is two times less than the second. The item was taken from the box for good luck. a) What is the probability that the item will be defective? b) the item was defective. What is the probability that it is made on the first machine.

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Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)