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.

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