Solving problem N3800 Bayesian probability theory

Solving problem N3800 Bayesian probability theory

3800. Of the 50 parts, 18 are 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. Taken part was excellent quality. What is the probability that the part is made in the second workshop?

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