Question

Your neighbor has an alarm system that has three alarms (main, backup, and second backup) with reliability of 80%, 70%, and 60%. Compute the probability of a system failure by creating a tree diagram.

Answer 1

Because the probabilities of success of the three alarms are 80%, 70%, and 60%, the probabilities of failure are 20%, 30%, and 40%, respectively. Multiply the three probabilities to find the probability of a system failure: 0.2 × 0.3 × 0.4 = 0.024. The probability of a system failure in this example is 2.4%.

Explanation: