Solution of problem N3785 probability theory total prob

Solution of problem N3785 probability theory total prob

3785. In the box there are 10 parts of factory No. 1, 15 parts of factory No. 2, and 25 parts of factory No. 3. The probabilities that a high-quality item is respectively 0.95 for the first plant, 0.85 for the second and 0.7 for the third. Find the probability that a piece taken out of the box at random will be of high quality.

Additional information:

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