Solving problem N3737 Bayesian probability theory

Solving problem N3737 Bayesian probability theory

3737. On the first machine, 20 parts were processed, 7 of them with a defect, 30 parts on the second, 4 of them are with defects, 50 are on the third, 10 of which are with defects. All parts are piled together. A piece taken at random was free from defects. 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)