Solving problem N3912 Bayesian probability theory

Solving problem N3912 Bayesian probability theory

3912. At the enterprise producing the bolts, the first machine produces 30%, the second 25%, and the third 45% of all products. Marriage in their products is respectively 2%, 1%, 3%. Find the probability that a random bolt, produced by a) the first, b) the second and c) by the third machine, turned out to be defective.

Additional information:

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