Solving problem N3912 Bayesian probability theory

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3912. At the enterprise producing the bolts, the first machine produces 30%, the second 25%, and the third 45% of all products. Marriage in their products is respectively 2%, 1%, 3%. Find the probability that a random bolt, produced by a) the first, b) the second and c) by the third machine, turned out to be defective.

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

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