Q.4.14 - A First Course in Probability

Question

On average, $5.2$ hurricanes hit a certain region in a year. What is the probability that there will be $3$ or fewer hurricanes hitting this year?

Step-by-Step Solution

Answer

$\text{ The required probability is }0.23807$

Step 1: Given Information

Given in the question that, on average, $5.2$hurricanes hit a certain region in a year.

We need to find the probability that there will be 3 or fewer hurricanes hitting this year. 

Step 2: Explanation

Here,

Average $=5.2$ hurricanes per year

That means the hurricane is likely to occur over a specified period.

Therefore, it is a Poisson distribution

Hence,

$P(3 or fewer hurricanes)$

$=P\left(0\right)+P\left(1\right)+P\left(2\right)+P\left(3\right)$

$=\frac{e^{-5.2}{5.2}^0}{0!}+\frac{e^{-5.2}{5.2}^1}{1!}+\frac{e^{-5.2}{5.2}^2}{2!}+\frac{e^{-5.2}{5.2}^3}{3!}$

$=0.238$

Step 3: Final Answer

The required probability is $0.23807$