The system shown below is a segment of a Parallel electrical circuit which has t

Question

The system shown below is a segment of a Parallel electrical circuit which has three relays. The current will flow from point (a) to point (b), that is system is working, if there is a closed path when the relays are switched to "on". However, the relays may malfunction. Suppose for each relay when it is switched to "on" the probability that each relay does not close and fail to work properly is 0.05, where relays are working independent to each others. a. Find the probability that system is working. b. Find the probability that the component 1 is working given that the system is working. (That is, find P(A_1 | B); where A_1 denote the event that the component one is working properly and B denotes the event that system is working.)

Explanation / Answer

a) probabilty that syestem is working =P(at least one relay is working )=1-P(none of relay is working)

=1-(0.05)3=0.999875

b)P(A1|B) =P(A, B and C are working ,A and B are working C not working , A an C are working B not working , A working and B and C are not working)/System is working

=(0.953+(0.95)2*0.05+(0.95)2*0.05+0.95*(1-0.05)2)/0.999875 =0.95/0.999875=0.950119

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