Solving problem N3661 Bayesian probability theory

Solving problem N3661 Bayesian probability theory

3661. From the first automatic machine on the assembly conveyor 19% of parts come from the 2nd and 3rd to 37% and 44% respectively. The probabilities of issuing defective parts are for each of them, respectively, 0.25%, 0.35% and 0.15%. The part received for assembly turned out to be defective. On which of the machines was most likely made?

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