Solving problem N3732 Bayesian probability theory

Solving problem N3732 Bayesian probability theory

3732. On three machines of different brands make the same type of parts. The performance of the 1st machine is 30 parts per shift, the 2nd and 3rd machines for 35 parts. It is established that defects have respectively 3% of parts manufactured on the first machine and 2% of parts manufactured on the second and third machines.
a) At the end of the shift, one part is taken at random for control. What is the probability that the item is taken without a defect?

Additional information:

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