Solving problem N3758 Bayesian probability theory

Solving problem N3758 Bayesian probability theory

3758. The assembly shop receives parts from three production lines. The performance of these lines are 5: 3: 2. The probability of rejection for the first line is 0.01, for the second - 0.02 and for the third line - 0.03. a) Find the probability that a part taken at random is defective. b) At random, the taken part turned out to be defective. Determine the probability that it is made on the third line.

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