Solving problem N3621 Bayesian probability theory

Solving problem N3621 Bayesian probability theory

3621. Three machines, the performance of which is referred to as 5: 3: 2, produce the same parts, with the first machine giving 70% of the highest grade parts, the second - 50%, the third - 60%.
a) find the probability that a part taken at random will be of the highest grade
b) the detail taken at random was of the highest grade. Find the probability that it is made on the third machine.

Additional information:

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

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