Question

One type of jet engine has a 0.0001 probability of failure while in flight. For a jet that has four of these engines, what is the probability of at least two of them failing?
Show all steps and explain how the answer was gotten

Answer 1

Let X denote the number of engines failing. Then, X~Binomial(n=4,p=0.0001)

$P(X=x)=\binom{4}{x}(0.0001)^{x}(1-0.0001)^{4-x},x=0,1,2,3,4$

Required probability =

$P(X\geq 2)=P(X=2)+P(X=3)+P(X=4)=\binom{4}{2}(0.0001)^{2}(1-0.0001)^{4-2}+\binom{4}{3}(0.0001)^{3}(1-0.0001)^{4-3}+\binom{4}{4}(0.0001)^{4}(1-0.0001)^{4-4}=5.9992\times 10^{-8}=0.000000059992$