Solution of problem N3787 probability theory total prob

Solution of problem N3787 probability theory total prob

3787. The box contains 12 parts manufactured at plant number 1, 20 parts are manufactured at plant number 2, and 18 parts are manufactured at plant number 3. The probability that a part manufactured at plant number 1 of excellent quality is 0.9; for parts manufactured at plants No. 2 and No. 3, these probabilities are 0.6 and 0.9, respectively. Find the probability that the item extracted at random will be of excellent quality.

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