Solving problem N3773 Bayesian probability theory

Solving problem N3773 Bayesian probability theory

3773. The store receives the products of three factories. Moreover, the production of the first factory is 20%, the second - 45% and the third - 35% of products. It is known that the average percentage of non-standard products for the first factory is 3%, for the second - 2%, and for the third - 4%. The probability that a non-standard product produced at the THIRD factory equals:

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