Solving problem N3683 Bayesian probability theory

Solving problem N3683 Bayesian probability theory

3683. Two automatic machines make identical details on the general conveyor. The performance of the first machine is three times the second. In addition, the first produces 72% of parts of excellent quality, the second - 82%. Find the probability that:
1) taken at random item of excellent quality;
2) and this item is made by the second machine.

Additional information:

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