Solution of problem N3954 probability theory total prob

Solution of problem N3954 probability theory total prob

3954. Electric bulbs are manufactured at three plants. The first produces 45% of the total number of light bulbs, the second - 40%, the third - 15%. The products of the first plant contain 30% of energy-saving lamps, the second-20%, and the third-25%. The store receives products from all three plants. What is the probability that a lamp purchased at the store will be energy efficient?

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