Solving problem N3859 Bayesian probability theory

Solving problem N3859 Bayesian probability theory

3859. The assembler received two boxes of identical parts manufactured by factory No. 1, and three boxes of the same parts manufactured by factory No. 2. The probability that a part of factory No. 1 is standard is 0.9, and that of factory No. 2 is 0.7. From a box of a box taken at random, a piece extracted by a collector turned out to be standard. What is more likely: this part is made by factory number 1 or number 2?

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