Ten engines undero testing If the failure probability that a

Ten engines undero testing. If the failure probability that an individual engine is 0.10, what is the probability that more than two engines will fail the test?

Solution

Given X~Binomial(n=10, p=0.1)

P(X=x)=10Cx*(0.1^x)*(0.9^(10-x))

So the probability that more than two engines will fail the test is

P(X>2) = 1-P(X=0)-P(X=1)-P(X=2)

=1-10C0*(0.1^0)*(0.9^(10-0))-10C1*(0.1^1)*(0.9^(10-1)) -10C2*(0.1^2)*(0.9^(10-2))

= 0.07019083