Solving problem N4261 Bayesian probability theory

Solving problem N4261 Bayesian probability theory

4261. The first factory manufactured 5000 devices, the second - 10000, the third - 2000. The first factory produces 1% of scrap, the second - 0.5%, the third - 1.5%. The device taken at random turned out to be defective. What is the likelihood that this device was manufactured by a second factory.

Additional information:

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