Solving problem N3818 Bayesian probability theory

Solving problem N3818 Bayesian probability theory

3818. In the workshop on the three machines manufactured the same type of parts. The probability of manufacturing a part on the first machine is 0.5, on the second - 0.3, on the third - 0.2. The probability of manufacturing a defective part on the first machine is 0.2; at the second 0.3; in the third 0.1. Find the probability that the selected part will be standard at random. What is the probability that this standard part is made on the third machine?

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