Solving problem N3776 Bayesian probability theory

Solving problem N3776 Bayesian probability theory

3776. The warehouse receives the products of three factories, the products of the first factory being 20%, the second 40% and the third 40%. It is known that the average percentage of non-standard products for the first factory is 3%, the second - 2%, and for the third - 1%. Find the probability that a product taken at random is produced at the 1st factory, if it turned out to be non-standard.

Additional information:

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