Solving problem N3918 Bayesian probability theory

Solving problem N3918 Bayesian probability theory

3918. The warehouse receives products from 3 factories. The production of the first plant amounts to 2000 products, the second one is 3000, the third one is 1000. It is known that the average percentage of non-standard products of the first plant is 4, the second is 2, and the third is 1. It is also known that the product taken at random is defective. Find the probability that this product is the first plant.

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