Question

In a​ 22-year period, a particular location was hit by 38 major hurricanes. Assume that major hurricanes are independent of each other and that the mean number of hurricanes per year has not changed.

​a) What's the probability of no hurricanes next​ year?

​b) What's the probability that during the next​ year, there is exactly one​ hurricane?

​c) What's the probability that during the next​ year, there is more than one​ hurricane?

Answer 1

Since, there were 38 major hurricanes in a 22-year period, the mean number of hurricanes per year is equal to 38/22 = 1.727273.

Now, let X denote the number of hurricanes next year and we are given that the mean number of hurricanes per year has not changed. Thus,

X ~ Poisson( = 1.727273)

and the probability mass function of X is given by:

a)

The probability of no hurricanes next year is given by:

b)

The probability that during the next year, there is exactly one hurricane is given by:

c)

The probability that during the next​ year, there is more than one​ hurricane is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.