Solution of problem N3916 probability theory total prob

Solution of problem N3916 probability theory total prob

3916. On three machines with identical and independent conditions, parts of the same name are manufactured. On the first machine make 14%, on the second - 34%, on the third - 52% of all parts. The probability of each part to be defect free is 0.53 if it is made on the first machine, 0.77 if it is made on the second machine, and 0.85 if it is on the third. Find the probability that a part taken at random will be defect free.

Additional information:

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