Question

A particular fault is supposed to trigger five redundant alarms. These alarms fail idependently. If the probabilities that alarms 1 and 2 will trigger when this fault occurs are 0.99 and 0.995, respectively, and that alarm 3-5 will not trigger when fault occurs are 0.01 for each one. What is the probability that no alarm will trigger when the fault occurs? What is the probability that all will trigger when the fault occurs?

Answer 1

Let us name the alarms as a,b,c,d,e

P(a) =0.99

P(b)=0.995

P(c) =1-0.01 =0.99

P(d) =1-0.01 =0.99

P(e) =1-0.01 =0.99

part A) What is the probability that no alarm will trigger when the fault occurs?

So,P(a' n b' n c' n d' n e') =P(a') *P(b') *P(c') *P(d') *P(e')

                                                            = (1-0.99)*(1-0.995)*0.01*0.01*0.01

                                                            =0.01*0.005*0.01*0.01*0.01

                                                            =5x10^(-11)

part B)

P(all alarms trigger) =P(a n b n c n d n e) =P(a) *P(b) *P(c) *P(d) *P(e)

                                                                                          =0.99*0.995*0.99*0.99*0.99

                                                                                          =0.95579303