Решение задачи N3966 теория вероятностей Байеса

3966. One-type products from three plants are on sale. Marriage respectively is 6, 6, 11%. 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 benign product.
2) Which plant most likely produced the purchased defective product.

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