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?

Anish Buchanan
2021-02-12
Answered

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Arham Warner

Answered 2021-02-13
Author has **102** answers

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,$\lambda =1$ per month.

For three months$\lambda =1\cdot 3=3.$

If X is the Poisson random variable, then the probability mass function of X is

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

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

$P(X>2)=1-P(X\le 2)$

$=1\{P(X=0)+P(X=1)+P(X=2)\}$

$=1-\{\frac{{e}^{-3}{3}^{0}}{0!}+\frac{{e}^{-3}{3}^{1}}{1!}+\frac{{e}^{-3}{3}^{2}}{2!}\}$

$=1-\{0.0498+0.1494+0.2240\}$

$=1-0.4232$

$=0.5768$

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,

For three months

If X is the Poisson random variable, then the probability mass function of X is

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

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

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