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Solving problem N3859 Bayesian probability theory

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