Solving problem N4007 Bayesian probability theory

Solving problem N4007 Bayesian probability theory

4007. The store receives the same type of products from three factories, with the 1st plant supplying 40% of the items, the 2nd plant - 30%, the 3rd plant - 30%. Among the products of the 1st plant 80% are top-notch, among the products of the 2nd - 80%, of the 3rd - 90%. Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is produced by the 1st plant.

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