A famous NBA player appears at a local hot spot an average once every month. What is the probability that he will make an appearce at this same local that hot spot more than 2 times in a three month span?

Let X be number of times a famous NBA player appears at a local hot spot.
Since this is a rare event, X follows Poisson distribution with mean 1. That is, ${\displaystyle \lambda =1}$ per month.
For three months ${\displaystyle \lambda =1\cdot 3=3.}$
If X is the Poisson random variable, then the probability mass function of X is
${\displaystyle P(X=x)=\frac{e^{-\lambda }{\lambda }^x}{x!},x=0,1,2}$,.......
Then, the probability that he will make an appearance at the local hot spot more than 2 times is
${\displaystyle P(X>2)=1-P(X\le 2)}$
${\displaystyle =1\{P(X=0)+P(X=1)+P(X=2)\}}$
${\displaystyle =1-\{\frac{e^{-3}{3}^0}{0!}+\frac{e^{-3}{3}^1}{1!}+\frac{e^{-3}{3}^2}{2!}\}}$
${\displaystyle =1-\{0.0498+0.1494+0.2240\}}$
${\displaystyle =1-0.4232}$
${\displaystyle =0.5768}$
Thus, the probability that he will make an appearance at the local hot spot more than 2 times is 0.5768.