Question

Your neighbor Philip buys a new alarm system that has two alarms (main and backup) with a 0.01 probability of a system failure. After reading the manual, he discovers that the second alarm has a 0.05 probability of failing. What is the probability of the first alarm failing?

Answer 1

0.2 or 20%... see image

Explanation:

Answer 2

0.2

Explanation:

Let P(A) = probability of first alarm failing and P(B) = probability of second alarm failing = 0.05. Since the events are independent, we have that the probability of both alarms failing or of system failure is P(A ∪ B) = P(A) × P(B).

Since the probability of both alarms failing or of system failure, P(A ∪ B) = 0.01, then the probability of the first alarm failing P(A) = P(A ∪ B)/P(B) = 0.01/0.05 = 0.2.

So, the probability of the first alarm failing P(A) = 0.2