Solving problem N3971 Bayesian probability theory

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3971. Single-type products from three plants are on sale. Marriage respectively is 3%, 1%, 8%. 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.

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

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