Solution of problem N3795 probability theory total prob

Solution of problem N3795 probability theory total prob

3795. Of the 70 parts, 20 are made in the first workshop, 25 in the second, the rest in the third. The first and third shops make products of excellent quality with a probability of 0.9, the second-0.75. What is the probability that the lucky part will be of excellent quality?

Additional information:

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