Solving problem N3817 Bayesian probability theory

Solving problem N3817 Bayesian probability theory

3817. The probability of a marriage in the manufacture of the product on the first machine is 0.02, on the second - 0.03, on the third 0.01. The performance of the first machine is twice as high as the second, and the performance of the third is three times greater than the first. Taken at random, the product was standard. 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)