Solving problem N3957 Bayesian probability theory

Solving problem N3957 Bayesian probability theory

3957. Electric bulbs are manufactured at three plants. The first plant produces 30% of the total number of light bulbs, the second - 25%, and the third - the rest. The products of the first plant contain 1% of defective light bulbs, the second - 1.5%, the third - 2%. The store receives products from all three plants. The lamp bought in the store turned out to be defective. What is the probability that it was produced by the first plant?

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