Solving problem N3809 Bayesian probability theory

Solving problem N3809 Bayesian probability theory

3809. The conveyor receives parts from two machines. The performance of the first machine is 2 times the performance of the second. The probability of marriage on the first machine is 0.01, on the second machine - 0.02. a) Find the probability that a piece taken at random is standard b) The piece taken was found to be standard. Determine the probability that it is made on the first machine.

Additional information:

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