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

Anish Buchanan

Answered question

2021-02-12

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?

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-02-13Added 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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?