Solving problem N3799 Bayesian probability theory

Solving problem N3799 Bayesian probability theory

3799. Of the 50 parts, 18 were made in the first workshop, 20 in the second, and the rest in the third. The first and third workshops give products of excellent quality with a probability of 0.9, the second with a probability of 0.6. Randomly taken detail was of excellent quality. What is the probability that it is made in the first shop?

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