Solving problem N3965 Bayesian probability theory

Solving problem N3965 Bayesian probability theory

3965. One-type products from three plants are on sale. Marriage respectively is 6%, 2%, 9%. The first plant supplies 40% of production, the second - 25%, the third - 35%. A single item is removed at random.
1) What is the probability to get a benign product;
2) Which plant most likely produced the purchased defective product.

Additional information:

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