Solution of problem N3797 probability theory total prob

Solution of problem N3797 probability theory total prob

3797. Of the 40 parts, 10 were made in the first workshop, 25 in the second, and the rest in the third. The first and third workshops give products of excellent quality with a probability of 0.9, the second workshop - with a probability of 0.7. What is the probability that the item taken at random will be of excellent quality?

Additional information:

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