Solving problem N3772 Bayesian probability theory

Solving problem N3772 Bayesian probability theory

3772. The warehouse receives the products of three factories. Moreover, the production of the first factory is 20%, the second - 45%, the third - 35%. In the production of the first factory 5% of non-standard products, in the production of the second - 2%, the third - 1%. A randomly taken product turned out to be standard. Find the probability that it was produced at the first factory.

Additional information:

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