Solving problem N4656 Bayesian probability theory

Solving problem N4656 Bayesian probability theory

4656. Parts for assembly are made on two machines, of which the first produces four times more than the second. In this case, the marriage is 0.005 in the output of the first machine, and 0.035 in the output of the second. A part taken at random turned out to be suitable for assembly. Find the probability that it was made on the first machine.

Additional information:

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