Solution of problem N3681 probability theory total prob

Solution of problem N3681 probability theory total prob

3681. Three automata stamp parts that are fed to a common conveyor. The performance of the first, second and third machines are 2: 3: 5. The probability of manufacturing a defective part by the first, second and third automata is 0.05; 0.1; 0.2. A detail was taken from the conveyor at random. Find the probability that it is not defective.

Additional information:

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