Find the indicated probabilities using the geometric distribution, the Poisson d

Question

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the last century, the mean number of major hurricanes to strike a certain country's mainland per year was about 0.61. Find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.

Explanation / Answer

Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is . Then, the Poisson probability is: P(x; ) = (e-) (x) / x! where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.

(a) P(X=1) = exp (-0.61)*(0.61)^1/(1!) = 0.3314

(b) P(at most one major hurricane will strike the mainland)
= P(X=0) + P(X=1)
= exp (-0.61)*(0.61)^0/(0!) + exp (-0.61)*(0.61)^1/(1!) = 0.8748

(c) P(more than 1 major hurricane will strike the mainland) = P(X>1) = 1 - P(X<=1)=1 - 0.8748 = 0.1252

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