Solving problem N3981 Bayesian probability theory

Solving problem N3981 Bayesian probability theory

3981. In the sale of the same type products from three plants. Marriage respectively is 2, 6, 7%. 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 purchase a defective product.
2) Which plant most likely produced an acquired good-quality product.

Additional information:

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