Solving problem N3741 Bayesian probability theory

Solving problem N3741 Bayesian probability theory

3741. From the first machine comes to the assembly of 80% of parts, and from the second - 20% of the same parts. On the first machine, the defect is 1%, and on the second - 5%. Proven detail was defective. What is more likely: this part is made on the first machine or is it made on the second machine?

Additional information:

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