Solving problem N3926 Bayesian probability theory

Solving problem N3926 Bayesian probability theory

3926. Two plants produce televisions. The first of them makes 70% of all products, the second 30%, with 90% of the products of the first plant and 85% of the second - of the highest quality. a) find the probability that the TV taken at random is of the highest quality. b) the TV selected at random turned out to be of the highest quality. What is the probability that it is made at the first plant?

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