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May 03'23
Exercise
An electronic system contains three cooling components that operate independently. The probability of each component’s failure is 0.05. The system will overheat if and only if at least two components fail.
Calculate the probability that the system will overheat.
- 0.007
- 0.045
- 0.098
- 0.135
- 0.143
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
May 04'23
Solution: A
The number of components that fail has a binomial(2, 0.05) distribution. Then,
[[math]]
\operatorname{P}( N ≥ 2)= p(2) + p(3) = \binom{3}{2}(0.05)^2(0.95) + \binom{3}{3}(0.05)^3 = 0.00725.
[[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.