Solving problem N3772 Bayesian probability theory

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3772. The warehouse receives the products of three factories. Moreover, the production of the first factory is 20%, the second - 45%, the third - 35%. In the production of the first factory 5% of non-standard products, in the production of the second - 2%, the third - 1%. A randomly taken product turned out to be standard. Find the probability that it was produced at the first factory.

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

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