Solving problem N3896 Bayesian probability theory

Solving problem N3896 Bayesian probability theory

3896. Three workers handle the same type of parts. The first one processed 20 parts for a shift, the second - 25, the third - 15. The probability of marriage for the first worker is 0.03, for the second - 0.02, for the third - 0.04. From the total output for a change at random, one detail was taken and tested, which turned out to be defective. Find the probability that it is processed by the second worker.

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