Решение задачи N3883 теория вероятностей Байеса

3883. For signaling a malfunction in the operation of an automated line, one indicator is used that belongs to probabilities of 0.2; 0.3; and 0.5 to one of three types, for which the probabilities of operation when the normal operation of the line is disturbed are equal to 0.99, respectively; 0.75 and 0.40. Find the probability that the indicator is triggered by a line fault. What is the probability that a type 1 indicator is used for control if it has signaled a malfunction that has occurred?

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