Solving problem N3888 Bayesian probability theory

Solving problem N3888 Bayesian probability theory

3888. The collector receives 50% of the details of Plant No. 1, 30% of Plant No. 2, 20% of Plant No. 3. The probability that a part of factory No. 1 is of excellent quality is 0.7; plant number 2 - 0.8; Plant number 3 - 0.9. The detail taken at random turned out to be of excellent quality. Find the probability that this part is made by factory number 1.

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