Answer
a. $\frac{1}{256}$
b. $\frac{1}{4096}$
c. $0.524$
d. $0.476$
Work Step by Step
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
$1-p(not\ 10)=1-0.524=0.476$
