Solving problem N3911 Bayesian probability theory

Solving problem N3911 Bayesian probability theory

3911. At the bolts factory, the first machine produces 25%, the second - 35%, the third - 40% of all products. In their products, the defect is respectively 5%, 4%, 2%. A random bolt turned out to be defective. What is the probability that it is made on the third machine?

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