Solving problem N4654 Bayesian probability theory

Solving problem N4654 Bayesian probability theory

4654. Parts for assembly are produced on two machines, of which the first produces parts 3 times larger than the second. In this case, the marriage is 0.025 in the output of the first machine, and 0.015 in the output of the second. One part taken at random turned out to be suitable for assembly. Find the probability that it was produced on the second machine.

Additional information:

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