Answer to Question #123446 in Statistics and Probability for Yasini

Question

A piece of equipment will function only when the three components A, B and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05 and that of C failing is 0.1. what is the probability that the equipment will fail before the end of the year?

Answer 1

the probablity of A failing =p(a)=0.15, not failing p(!a)=0.85

the probablity of b failing =p(b)=0.05, not failing p(!b)=0.95

the probablity of c failing =p(c)=0.10, not failing p(!c)=0.90

the probability that the equipment will fail in one year is (0.15*0.95*0.90)+(0.85*0.05*0.90)+(0.85*0.95*0.10)=0.247