A Define all relevant elemental events and express the numbe

A) Define all relevant elemental events and express the numbers given as probabilities of events.

B) Express the event that the circuit operates in set notation (intersections, unions, etc. of elemental events).

C) What is the probability that the circuit operates? Note --> it’s much easier to directly find the probability that it operates, than to first find the probability that it does not operate. (Since each component operates independently, groups of components also operate independently as long as the same component does not appear in more than one group, and you can use the multiplicative rule for the intersection of groups of events)

The following circuit operates if and only if there is a path of functional devices from left to right. Assume devices fail independently and that the probability of failure of each device is as shown. 0.02 0.02 0.2 0.2 0.2

Solution

a)

P(A) = 0.02

P(B) = 0.02

P(C)= 0.2

P(D)= 0.2

P(E)= 0.2

For each part of this loop, the probability that it functions is 1 minus the probability that both elements fail:

P(loop 1 ) = 1- (1-0.04)(1-0.02) = 0.0592

P( loop 2 ) = 1 - (1-0.02)(1-0.02) = 0.0396

P (circuit functions) = P (loop 1)*P (loop 2) = 0.0592*0.0396 = 0.00234432

B)

I can gladly help you but you should post it in a new question. Thank you!