Question

Suppose that at a busy traffic junction, the probability p of an individual car having

an accident is 0.0001. During a certain part of the day, 100 cars pass through the

junction. What is the probability of two or more cars being involved in an accident

within this period?

Answer 1

$\lambda=0.0001\times 100=0.01\\ P(X\geq 2)=1-P(X<2)\\ =1-[P(X=0)+P(X=1)]\\ =1-[\frac{e^{-0.01}(0.01)^{0}}{0!}+\frac{e^{-0.01}(0.01)^{1}}{1!}]\\ =1-0.99995=0.00005$