Solution of problem N3726 probability theory total prob

Solution of problem N3726 probability theory total prob

3726. The probabilities that during the operation of an electronic device a failure occurs in an arithmetic device, in RAM, in other devices are referred to as 5: 6: 2. What is the probability that a failure occurring in a device will be detected if the probability of detecting a failure in an arithmetic device, in RAM, in other devices are respectively 3/5, 0.6, 0.8?

Additional information:

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