Решение задачи N3967 теория вероятностей Байеса

3967. One-type products from three plants are on sale. Marriage respectively is 2, 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 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)