Solving problem N3929 Bayesian probability theory

Solving problem N3929 Bayesian probability theory

3929. Three factories make identical products. The first plant produces 20% of the total production, the second - 30%, the third - 50%. The probability of the product of the first plant to be defective is 0.2, the product of the second plant is 0.1, the product of the third plant is 0.05. 1) What is the probability that at random the selected product will be defective? 2) What is the probability that it is made by a third plant?

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