Solving problem N3876 Bayesian probability theory

Solving problem N3876 Bayesian probability theory

3876. A batch of parts is made by three workers, with the first worker producing 25% of all parts, the second - 35%, the third - 40%. In the production of the first labor defect is 5%, in the production of the second 4% and in the production of the third 2%. The item randomly selected for control was defective. What is the probability that it is made by the second worker?

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