Solution of problem N3794 probability theory total prob

Solution of problem N3794 probability theory total prob

3794. The box contains 16 parts of factory No. 1, 20 parts of factory No. 2, 24 parts of factory No. 3. The probability that parts of factory No. 1 are of excellent quality is 0.9; for parts of factories No. 2 and No. 3, it is 0.65 and 0.92, respectively. Find the probability that the item extracted at random will be of excellent quality.

Additional information:

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