Causes of death. Government data assign a single cause for each death
that occurs in the United States. The data show that the probability is 0.34 that
a randomly chosen death was due to heart disease, and 0.23 that it was due to
cancer. What is the probability that a death was due either to heart disease or
to cancer? What is the probability that the death was due to some other cause?

18.8 High school academic rank. Select a first-year college student at ran-
dom and ask what his or her academic rank was in high school. Here are the
probabilities, based on proportions from a large sample survey of first-year stu-
dents:
Rank: Top 20% Second 20% Third 20% Fourth 20% Lowest 20%
Probability: 0.44 0.26 0.23 0.06 0.01
(a) What is the sum of these probabilities? Why do you expect the sum to have
this value?
(b) What is the probability that a randomly chosen first-year college student
was not in the top 20% of his or her high school class?
(c) What is the probability that a first-year student was in the top 40% in high
school?