Solving problem N3651 Bayesian probability theory

Solving problem N3651 Bayesian probability theory

3651. From the first automatic machine on the assembly conveyor 15% of parts go from 2nd and 3rd to 35% and 50%, respectively. The probabilities of issuing defective parts are for each of them, respectively, 0.3%, 0.35% and 0.05%. Find the probability that the part arriving at the assembly will be defective, as well as the likelihood that it was made on the 1st, 2nd and 3rd automatic machine tools, provided that it turned out to be defective.

Additional information:

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