## Precalculus (6th Edition) Blitzer

a. $\frac{1}{256}$ b. $\frac{1}{4096}$ c. $0.524$ d. $0.476$
Given that the probability that South Florida will be hit by a major hurricane in any single year is $p=\frac{1}{16}$, we have: a. the probability that South Florida will be hit by a major hurricane two years in a row is $p(2)=p\times p=\frac{1}{256}$ b. the probability that South Florida will be hit by a major hurricane in three consecutive years is $p(3)=p\times p\times p=\frac{1}{4096}$ c. the probability that South Florida will not be hit by a major hurricane in the next ten years is $p(not\ 10)=(p(not\ 1))^{10}=(1-p)^{10}=(\frac{15}{16})^{10}\approx0.524$ d. the probability that South Florida will be hit by a major hurricane at least once in the next ten years is $1-p(not\ 10)=1-0.524=0.476$