Solving problem N3653 Bayesian probability theory

Solving problem N3653 Bayesian probability theory

3653. From the first automatic machine on the assembly conveyor 15% of parts come in, from the 2nd and 3rd - 46% and 39% respectively. The probability of issuing defective parts are for each of them, respectively, 0.25%, 0.35% and 0.15%. The part received for assembly turned out to be defective. Which machine was it most likely made on?

Additional information:

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