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
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]]