Hurricanes
A company prices its hurricane insurance using the following assumptions:
i.
In any calendar year there can be at most one hurricane in any given location.
ii.
In any calendar year, the probability of a hurricane at any given location is 0.05.
iii.
The number of hurricanes in any calendar year is independent of the number of hurricanes in
any other calendar year.
Find the probability of fewer than three hurricanes in a twenty year period.
To apply binomial probability, we must first establish whether this problem can be considered a
binomial experiment. A binomial experiment must satisfy three conditions.
1. The same experiment is repeated a fixed number of times.
2. There are only two possible outcomes, success or failure.
3. The repeated trials are independent, so that the probability of success remains the same for
each trial.
Let’s consider each trial of the experiment to be a calendar year and whether there is a hurricane at a
given location or not. In this case, we think of success as there is a hurricane at the location in the
calendar year and failure is that there is not a hurricane at the location in a given year. With this
definition, the experiment is repeated twenty times (for the twenty year period). Since the number of
hurricanes in a given year is independent of the number of hurricanes in another year, these trials are
part of a binomial experiment.
The event “fewer than three hurricanes in a twenty year period” is formed from three mutually
exclusive events,

“no hurricanes in a twenty year period”

“exactly one hurricane in twenty year period”

“exactly two hurricanes in a twenty year period”
We can find the probability of each of these events using binomial probability:
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Hurricanes
These mutually exclusive events form the event “fewer than three hurricanes in a twenty year period”
so
(
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The key to this problem is to determine if the problem corresponds to a binomial experiment and then
to write the event as a union of other mutually exclusive events.