Solving problem N3646 Bayesian probability theory

Solving problem N3646 Bayesian probability theory

3646. 40% come from the first automatic machine for assembly, 35% from the second, 25% from the third. Among the parts of the first machine, 0.2% is defective, the second is 0.3%, and the third is 0.5%. Find the probability that: a) the item received at the assembly is defective; b) the item turned out to be defective made on the second machine.

Additional information:

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