Solving problem N3827 Bayesian probability theory

Solving problem N3827 Bayesian probability theory

3827. Casting in blanks comes from two shops: 60% from the first shop and 40% from the second. Casting of the first workshop has 5% of the marriage, the second - 10% of the marriage. Taken at random, the disc turned out to be without defect. What is the probability that it is made by the first shop?

Additional information:

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