Solving problem N3895 Bayesian probability theory

Solving problem N3895 Bayesian probability theory

3895. Two automatic machines produce parts that are fed to a common conveyor. The probability of obtaining a non-standard part on the first automatic machine is 0.075, and on the second - 0.08. The performance of the second is three times greater than the first. Find the probability that a piece taken from the conveyor is non-standard. What is the probability that it is produced by the 1st machine?

Additional information:

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