Solving problem N3626 Bayesian probability theory

Solving problem N3626 Bayesian probability theory

3626. The assembly receives parts from three machines. The first machine gives 25%, the second - 30%, the third - 45% of parts of this type, received for the assembly. The first produces 0.1%, the second - 0.2%, the third - 0.3% non-standard parts. Find the probability that the non-standard part turned out to be made by the first machine gun.

Additional information:

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