Solving problem N3935 Bayesian probability theory

Solving problem N3935 Bayesian probability theory

3935. Watches are made in three factories and go to the store. The first plant produces 40% of products, the second - 45%, the third - 15%. In the production of the first plant, 80% of hours rush, the second - 70%, the third - 90%. What is the probability that the purchased watch is not in a hurry? If the purchased watches are in a hurry, then at what factory are they most likely made?

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