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Solving problem N3970 Bayesian probability theory

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3970. In the sale of the same type products from three plants. Marriage at each plant is 5, 5, 7%. The first plant supplies 25% of products, the second - 30%, the third - 45% of products. A single item was removed at random.
a) What is the probability of removing a defective product?
b) Which plant most likely produced the extracted good-quality product?
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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