Solving problem N3845 Bayesian probability theory

Solving problem N3845 Bayesian probability theory

3845. It is known that the probability of manufacturing a top-quality part is equal to 0.92 on the first machine, 0.8 on the second. Non-sorted parts made on both machines are in stock. Among them, the parts made on the first machine are 3 times more than the parts made on the second. Randomly taken detail was defective. Find the probability that it is made on the second machine.

Additional information:

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