Solving problem N4003 Bayesian probability theory

Solving problem N4003 Bayesian probability theory

4003. The shop receives similar products from three plants, with the i-th (i = 1,2,3) plant supplying mi percent of the products (m1 = 50%, m2 = 30%, m3 = 20%). Among the products of the i-th plant, ni percent are first-rate (70%, 80%, 90%). Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is released by the 3rd plant.

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