Solving problem N3738 Bayesian probability theory

Solving problem N3738 Bayesian probability theory

3738. The first machine handled 30 parts, 10 of them with defects, the second processed 40 parts, 5 of them with defects. On the third - 20 parts, from them 3 with defects. All parts are piled together; The item taken at random was free from defects. What is the probability that it is processed on the third machine?

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