Solving problem N3780 Bayesian probability theory

Solving problem N3780 Bayesian probability theory

3780. The warehouse receives the products of three factories, the products of the first factory being 40%, the second - 20%, and the third 40%. It is known that the average percentage of non-standard products for the first factory is 0.4%, for the second - 0.3%, for the third - 0.2%. It was a non-standard products. Find the probability that the randomly selected product will be the production of the first factory.

Additional information:

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