Solving problem N3781 Bayesian probability theory

Solving problem N3781 Bayesian probability theory

3781. The warehouse received the products of three factories. The production volumes of the first, second and third factories are respectively 2: 5: 3. It is also known that the average percentage of non-standard products among the products of the first factory is - 3, the second - 2, 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)