Solving problem N3878 Bayesian probability theory

Solving problem N3878 Bayesian probability theory

3878. Some product can be processed for random processing at one of three machines with probabilities equal to 0.2; 0.3; 0.5 When processing on the first machine, the probability of marriage is 0.02, on the second machine, 0.03 and on the third machine, 0.05. Find the probability that:
1) the product arrived at the workshop after processing meets the technical conditions;
2) the product was processed on the second machine.

Additional information:

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