Solving problem N4049 Bayesian probability theory

Solving problem N4049 Bayesian probability theory

4049. The shop receives the same type of products from three factories, with the i-th (i = 1,2,3) plant supplying mi percent of the products (10%, 50%, 40%). Among the products of the i-th plant, ni percent are first-rate (70%, 90%, 80%). Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is produced by the 2nd plant.

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