Solving problem N3927 Bayesian probability theory

Solving problem N3927 Bayesian probability theory

3927. Two plants produce refrigerators. The first of them makes 60% of all products, the second - 40%, with 80% of products of the first plant and 90% of the second - of the highest quality. a) Find the probability that a fridge of the highest quality is taken at random. b) The refrigerator chosen at random turned out to be top notch. What is the probability that it is made at the second plant?

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