Solving problem N3901 Bayesian probability theory

Solving problem N3901 Bayesian probability theory

3901. In the box there are parts of three types: 40 parts of the first type; 50 - the second and 60 - the third, and painted among them are, respectively, 20%, 40% and 60%. a) Find the probability that a piece extracted from a box is colored at random. b) At random, the extracted part was painted. Find the probability that this is a second type item.

Additional information:

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