Solving problem N3881 Bayesian probability theory

Solving problem N3881 Bayesian probability theory

3881. To signal that the operation mode of the automatic device deviates from the norm, an indicator is used, which with probabilities 0.3; 0.1; 0.6 belongs to one of three types. The probabilities of the indicator triggering when the normal operation of the device is disrupted are, respectively, 0.98; 0.92; 0.95. Find the probabilities that:
1) a signal is received from the indicator;
2) and this signal is received from the indicator of the second type.

Additional information:

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