Solving problem N3770 Bayesian probability theory

Solving problem N3770 Bayesian probability theory

3770. The warehouse receives products from 3 factories. Moreover, the production of the first factory is 20%, the second - 46%, and the third - 34%. It is known that the percentage of non-standard products for the first factory is 3%, for the second 2%, and for the third - 1%. Find the probability that a product taken at random is produced at the first 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)