Solving problem N3875 Bayesian probability theory

Solving problem N3875 Bayesian probability theory

3875. A batch of parts is made by three workers, the first having produced 35% of all the parts, the second 40%, the third - all the rest of the products. Marriage in their products is at the first - 2%, at the second - 3%, at the third - 4%. The item randomly selected for control was defective. What is the probability that it is made by a third worker?

Additional information:

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