Solving problem N3778 Bayesian probability theory

Solving problem N3778 Bayesian probability theory

3778. The shop receives the products of three factories. Moreover, the production of the first factory is 25%, the second - 40%, and the third - 35% of products. The average reject rate for the first factory is 2%, for the second - 3% and for the third - 4%. The probability that a defective product is produced at the first factory is equal to

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