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

\(\displaystyle{P}{\left({X}={x}\right)}=\frac{{{e}^{-\lambda}\lambda^{x}}}{{{x}!}},{x}={0},{1},{2}\),.......

Then, the probability that he will make an appearance at the local hot spot more than 2 times is

\(\displaystyle{P}{\left({X}>{2}\right)}={1}-{P}{\left({X}\le{2}\right)}\)

\(\displaystyle={1}{\left\lbrace{P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}\right\rbrace}\)

\(\displaystyle={1}-{\left\lbrace\frac{{{e}^{{-{3}}}{3}^{0}}}{{{0}!}}+\frac{{{e}^{{-{3}}}{3}^{1}}}{{{1}!}}+\frac{{{e}^{{-{3}}}{3}^{2}}}{{{2}!}}\right\rbrace}\)

\(\displaystyle={1}-{\left\lbrace{0.0498}+{0.1494}+{0.2240}\right\rbrace}\)

\(\displaystyle={1}-{0.4232}\)

\(\displaystyle={0.5768}\)

Thus, the probability that he will make an appearance at the local hot spot more than 2 times is 0.5768.

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

\(\displaystyle{P}{\left({X}={x}\right)}=\frac{{{e}^{-\lambda}\lambda^{x}}}{{{x}!}},{x}={0},{1},{2}\),.......

Then, the probability that he will make an appearance at the local hot spot more than 2 times is

\(\displaystyle{P}{\left({X}>{2}\right)}={1}-{P}{\left({X}\le{2}\right)}\)

\(\displaystyle={1}{\left\lbrace{P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}\right\rbrace}\)

\(\displaystyle={1}-{\left\lbrace\frac{{{e}^{{-{3}}}{3}^{0}}}{{{0}!}}+\frac{{{e}^{{-{3}}}{3}^{1}}}{{{1}!}}+\frac{{{e}^{{-{3}}}{3}^{2}}}{{{2}!}}\right\rbrace}\)

\(\displaystyle={1}-{\left\lbrace{0.0498}+{0.1494}+{0.2240}\right\rbrace}\)

\(\displaystyle={1}-{0.4232}\)

\(\displaystyle={0.5768}\)

Thus, the probability that he will make an appearance at the local hot spot more than 2 times is 0.5768.