It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. If one extra component is installed as a backup, what is the probability of at least one of the two components working for at least 60 hours?
A) About 0.51
B) About 0.09
C) About 0.06
D) About 0.70

Question

Quizplus · Accepted Answer

The probability of one component working for at least 60 hours is 1 - P(X < 60) = 1 - (1 - e^(-60/50)) = e^(-60/50) = 0.5134. The probability of both components working for at least 60 hours is (e^(-60/50))^2 = 0.2634. Therefore, the probability of at least one component working for at least 60 hours is 1 - 0.2634 = 0.7366.

It Is Assumed That the Time Failures for an Electronic