Solving problem N3779 Bayesian probability theory

Solving problem N3779 Bayesian probability theory

3779. The warehouse receives the products of three factories. Moreover, the production of the first factory is 26%; the second is 40%; the third is 34%. It is also known that the average percentage of non-standard products for the first factory is 1%; for the second - 3%; and for the third - 1.5%. Calculate the probability that a product taken at random was 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)