Solving problem N3716 Bayesian probability theory

Solving problem N3716 Bayesian probability theory

3716. Two punchers stuffed on different punchers on the same set of punched cards. The probability that the first puncher made a mistake is 0.15, the second 0.1. What is the probability that when checking at random the punched card turned out to be with an error? What is the probability that this punch card was stuffed with the first puncher?

Additional information:

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