Solving problem N3652 Bayesian probability theory

Solving problem N3652 Bayesian probability theory

3652. From the first automatic machine on the assembly conveyor 15% of parts go from the second and third to 35% and 50%, respectively. The probabilities of issuing defective parts are for each of them, respectively, 0,2; 0.05 and 0.098. Find the probability that the part received at the assembly will be defective and it is made on the second machine.

Additional information:

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