Solving problem N3743 Bayesian probability theory

Solving problem N3743 Bayesian probability theory

3743. From the first machine comes 70, from the second 30 of the same parts. On the first machine, the defect is 3%, on the second 2%. Proven detail was benign. What is the probability that it is made the first machine.

Additional information:

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