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

The aim is to find $P(X\geq2)$. Since $X$ takes values from to $100$ and $P(0\leq\! X\!\leq100)=1,$ we get the following formula for $P(X\geq2)$ :$P(X\geq2)=1-P(X=0)-P(X=1)=1-C_{100}^0(1-p)^{100}-C_{100}^1(1-p)^{99}p=$

$=1-(0.9999)^{100}-0.01\cdot(0.9999)^{99}\approx0.00005.$

The latter is rounded to 5 decimal places.

Answer: 0.00005