Решение задачи N3880 теория вероятностей Байеса

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.

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