Solving problem N3624 Bayesian probability theory

Solving problem N3624 Bayesian probability theory

3624. Gear assembly comes from three machines. The performance of the machines is 5: 6: 9. The first automatic machine allows 0.1% of marriage, the second - 0.2%, the third - 0.3%. Find the probability that the defective part arriving at the assembly, made the first machine.

Additional information:

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