Solving problem N3951 Bayesian probability theory

Solving problem N3951 Bayesian probability theory

3951. Electric bulbs are manufactured at three plants. The first plant produces 35% of the total number of light bulbs, the second - 50% and the third - 15%. The production of the first plant contains 70% of standard lamps, the second - 80% and the third - 90%. The store receives products from all three plants. What is the probability that a) a lamp taken at random is standard; b) standard electric lamp made at the second plant?

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