Solving problem N3880 Bayesian probability theory

Solving problem N3880 Bayesian probability theory

3880. Procurement can be received for processing on one of three machines with probabilities of 0.4; 0.25 and 0.35 respectively. When processing on the first machine, the probability of marriage is 1.2%, on the second - 2%, on the third - 1.8%. Find the probability that:
a) randomly taken after processing the product is standard;
b) at random, the product taken after processing turned out to be standard. What is the probability that it is processed on the third machine.

Additional information:

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