Solving problem N3862 Bayesian probability theory

Solving problem N3862 Bayesian probability theory

3862. The collector received 14 boxes of parts manufactured by plant number 1 and 16 boxes of parts manufactured by plant number 2. The probability that a part of factory number 1 is standard is 0.75, and that of factory number 2 is 0.8. The collector picked up the item at random from the box taken at random. Extracted non-standard part. Determine the probability that it is made by the factory №1.

Additional information:

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