Solution of problem N3798 probability theory total prob

Solution of problem N3798 probability theory total prob

3798. Of the 50 parts, 18 were made in the first workshop, 20 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 with a probability of 0.6. What is the probability that a piece taken at random will be of excellent quality?

Additional information:

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