Solving problem N3930 Bayesian probability theory

Solving problem N3930 Bayesian probability theory

3930. Three car-building factories produce the same products, the first factory producing 50%, the second 20%, and the third 30% of all products. The first plant produces 1% of the marriage, the second plant - 2% and the third - 3%. At random, the selected wagon was left with a marriage. Find the probability that the car is produced by the second plant.

Additional information:

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