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
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?
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Expert Answer

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, λ=1 per month.
For three months λ=13=3.
If X is the Poisson random variable, then the probability mass function of X is
P(X=x)=eλλxx!,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)=1P(X2)
=1{P(X=0)+P(X=1)+P(X=2)}
=1{e3300!+e3311!+e3322!}
=1{0.0498+0.1494+0.2240}
=10.4232
=0.5768
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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