Solving problem N3955 Bayesian probability theory

Solving problem N3955 Bayesian probability theory

3955. The light bulbs of three plants come into the store. The first plant produces 45% of all products, the second 40% and the third 15%. The production of the first plant contains 70% of standard lamps, the second 80%, the third 81%. The lamp purchased in the store turned out to be standard. What is the probability that it is made at the first plant?

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