Solving problem N3620 Bayesian probability theory

Solving problem N3620 Bayesian probability theory

3620. Among the parts arriving at the assembly from the first machine gun, 85% are of excellent quality, for the second and third machine parts of excellent quality, respectively, 94% and 79% come. The performance of these machines are 4: 5: 3. Find the probability that: 1) taken at random item of excellent quality; 2) and made the second machine.

Additional information:

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