Solving problem N3662 Bayesian probability theory

Solving problem N3662 Bayesian probability theory

3662. From the first automatic machine on assembly 20% come, from the second - 30%, from the third - 50% of details. The first machine gives an average of 0.2% of the marriage, the second - 0.3%, the third - 0.1%. Find the probability that the defective part is made on the second machine.

Additional information:

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