Solving Problem N3619 Bayesian Probability Theory

Solving Problem N3619 Bayesian Probability Theory

3619. Among those entering the assembly of parts from the first machine gun are 83% of excellent quality, from the second and third machines of similar parts of excellent quality 92% and 89%. The performance of these machines are referred to as 3: 2: 5, respectively. Find the probability that the item taken at random: 1) excellent quality; 2) and made on the first machine.

Additional information:

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