The probability of any one of the pumps failing during the storm is 1/8. What is the probability that at least 2 pumps will be working.

Given n= 5

p = 1/8 = 0.125

q= 1-p

q= 1-0.125

q= 0.875

For at least two pumps will be working, hence r = 2.,3,4,5. Hence, for simplification in calculation, we first find r=0 and r=1, than substrate with 1, to obtain the probability.

By binomial distribution

$\begin{equation} P(X=r) = n_{c_r}p^rq^{n-r} \\ P(X=r=0,1) = 5_{c_0}(0.125)^0 (0.875)^5 + 5_{c_1}(0.125)^1 (0.875)^4\\ P(X=r=0,1) = 0.5129 +0.36636 \\ P(X=r=0,1) = 0.879 \text{Hence for at least two pump will working,}\\ P(X=r=2,3,4,5) = 1- P(X=r=0,1) \\ = 1- 0.879 \\ P(X=r=2,3,4,5) = 0.1205 \\ \end{equation} $