Solving problem N3815 Bayesian probability theory

Solving problem N3815 Bayesian probability theory

3815. Workers service three machines on which the same parts are processed. The probability of manufacturing a defective part is 0.02 on the first machine, 0.03 on the second, 0.04 on the third. The machined parts are folded in one drawer. The performance of the first machine is three times more than the second, and the third is two times less than the second. Taken for good luck item was defective. Find the probability that it is made on the third machine.

Additional information:

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