Solving problem N3724 Bayesian probability theory

Solving problem N3724 Bayesian probability theory

3724. The likelihood that during the operation of a digital electronic machine will fail in the arithmetic unit, in RAM, in other devices, refer to 2: 4: 5. The probability of detecting a failure in an arithmetic unit, in the RAM and other devices, respectively, is 0.75; 0.8; 0.9. Find the probability that:
1) a malfunction that occurred in the car is detected;
2) failure occurred in RAM.

Additional information:

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