Solving problem N3913 Bayesian probability theory

Solving problem N3913 Bayesian probability theory

3913. In a bolts factory, the first machine produces 25%, the second - 35%, and the third - 40% of all bolts. In their products, the defect is respectively 5, 4 and 7%. a) Find the probability that a randomly selected bolt was defective. b) A randomly selected bolt was found to be defective. Find the probability that it is manufactured by the first machine.

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