Solving problem N3728 Bayesian probability theory

Solving problem N3728 Bayesian probability theory

3728. The assembly received 100 of the same type of parts: 40 parts are made on the first machine, of which 65% of the first-class parts; 25 parts are made on the second machine, of which 57% of parts of the first grade; 35 parts are made on the third machine, 72% of them are first-class parts. The collector took the detail at random. Find the probability that:
1) the taken detail of the first grade;
2) and made on the second machine.

Additional information:

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