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(a) An electrical component is made up of two independent circuits, C1 and C2 which are designed to last for a year
(a) An electrical component is made up of two independent circuits, C1 and C2 which are designed to last for a year. In the past, circuit Cl has 95% chance of lasting for a year while circuit C2 has 96% chance of lasting for a year. The electrical component will work as long as one of the circuits is still working. Find the probability that at the end of a year (i) both circuits are working, (3 marks) (ii) the electrical component is working. (3 marks)
Expert Solution
(i) Probability that both circuits are working =0.912
(ii) The probability that the electrical component is working =0.998
Step-by-step explanation
Probability that circuit C???????1 is working , P(C1) =95% =0.95
Probability that circuit C???????2 is working , P(C2) =96% =0.96
(i) Probability that both circuits are working =P(C1) × P(C2) =0.95×0.96 =0.912
(ii) Probability that circuit C???????1 is not working = 1- P(C1) =1-0.95 =0.05
Probability that circuit C???????2 is not working =1- P(C2) =1-0.96 =0.04
So, probability that none of the circuits are working =0.05×0.04 =0.002
So, probability that at least one of the circuits is working = 1 -probability that none of the circuits are working =1-0.002 =0.998
The electrical component will work as long as one of the circuits is still working.
So, probability that the electrical component is working = probability that at least one of the circuits is working =0.998
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