A major hurricane is a hurricane with a wind speed of 111 miles per hour or greater. During the last century, the mean number of major hurricanes to strike a certain countries mainland per year was about 0.54. Find the probability that in a given year.
(a) exact one major hurricane will strike the mainland (b) at most one major hurricane will strike the main land (c) more that one major hurricane will strike the mainland
A sensible way to model this problem is using the Poisson distribution (which gives a number of events in a certain time frame).
So if the mean number of hurricanes is 0.54, this will be lambda in our poisson distribution formula. So we can find the probability of seeing exactly h hurricanes using:
P( h ; lambda ) = (e-lambda) (lambdah) / h!
We can work all this out by hand, or we can just use a built-in function (e.g. in google sheets use =poisson(h,lambda,0); the final 0 just means you're using the pdf not the cdf, i.e. finding the probability of a single number, not a range).
a) P( h=1 ; lambda=0.54 ) = 0.3147
b) This is either the cdf of the poisson at 1 (in sheets use =poisson(1,0.54,1), or you can find the probability of getting zero hurricanes (=poisson(0,0.54,0)) and add it to the probability of getting 1, above. Either way:
P( h<=1 ; lambda=0.54 ) = 0.8974
c) This is just the inverse of the previous answer, right? So subtract 0.8974 from 1: