Question

tourists enter a popular game reserve at an average rate of one every five minutes. what is the probability that it takes more than twenty minutes until the first tourist arrives?

Answer 1

Let $X=$ the number of tourist arrives: $X\sim Po(\lambda t)$

Given $\lambda=1, t=4$

$$P(X=0)=\dfrac{e^{-\lambda t}\cdot(\lambda t)^0}{0!}=e^{-1(4)}\approx0.018316$$

The probability that it takes more than twenty minutes until the first tourist arrives is

$0.018316.$