Solution of problem N3793 probability theory total prob

Solution of problem N3793 probability theory total prob

3793. The kit consists of 16 parts of plant number 1, 12 parts of plant number 2 and 22 parts of plant number 3. The probabilities that a part of low quality is 0.08 for the first plant, 0.06 for the second plant and 0.1 for the third. Find the probability that a piece taken out of the kit at random will be of high quality.

Additional information:

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