Solving problem N3722 Bayesian probability theory

Solving problem N3722 Bayesian probability theory

3722. The probabilities that during the operation of a digital electronic machine a malfunction will occur in the arithmetic unit, in the operative memory, in other devices, refer to as 3: 2: 4. The probability of detecting a failure in these devices is respectively 0.75; 0.8; 0.9. Find the probability that:
1) a malfunction that occurred in the car is detected;
2) and originated in the arithmetic unit.

Additional information:

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