Solving problem N3864 Bayesian probability theory

Solving problem N3864 Bayesian probability theory

3864. The assembler has 3 boxes of parts manufactured by factory No. 1 and 4 manufactured by factory No. 2. The probability that the detail of plant number 1 is standard is 0.7, and plant number 2 is 0.9. Randomly, the extracted part from the randomly taken box turned out to be standard. Find the probability that the item is made by factory №1.

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