Решение задачи N3881 теория вероятностей Байеса

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.

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