Solution of problem N3784 probability theory total prob

Solution of problem N3784 probability theory total prob

3784. In the box there are 10 parts manufactured in workshop No. 1, 25 parts manufactured in workshop No. 2, and 15 parts manufactured in workshop No. 3. The probability of rejection for parts of workshop No. 1 is 0.02, workshop No. 2 is 0.05, and workshop No. 3 is 0.01. A part has been removed from the box. Find the probability that it is benign.

Additional information:

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