Solution of problem N3819 probability theory total prob

Solution of problem N3819 probability theory total prob

3819. In the workshop on three machines manufactured the same type of parts. The probability of failure-free operation of the first machine is 0.3, the second - 0.4, the third - 0.3. The probability of manufacturing a defective part on the first machine is 0.2, on the second - 0.3, on the third - 0.1. Find the probability that the selected part will be standard at random.

Additional information:

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