Solving problem N3933 Bayesian probability theory

Solving problem N3933 Bayesian probability theory

3933. There are three factories producing the same products. At the same time, the first plant produces 50%, the second plant - 30%, and the third plant - 20% of the total output. Marriage is 2% of the output of the 1st plant, 3% of the output of the 2nd and 4% of the output of the 3rd plant. All products are mixed and marketed. Find the conditional probability that the purchased product is manufactured by the first factory, if this product is defective.

Additional information:

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