Chapter 3.6, Problem 46E

Figure 3.51 gives the estimated number of diagnoses of AIDS in the United States by age at the time of diagnosis in 2011. Also note that in 2011, there were 301, 621, 157 residents of the United States, according to the U.S. Census Bureau.

Age (in years)	Cumulative number of AIDS cases
Under 13	15
13-14	49
15-24	2, 935
25-34	7, 434
35-44	8, 874
45-54	8, 561
55-64	3, 305
65 or older	899

Figure 3.51 AIDS by age. Source: Centre for Disease Control and Prevention

a. Find the probability that a U.S. resident diagnosed with AIDS was 15 to 24 years old at the time of diagnosis.

b. Find the probability that a U.S. resident was diagnosed with AIDS and was 15 to 24 years old at the time of diagnosis.

c. Find the probability that a U.S. resident diagnosed with AIDS was 25 to 34 years old at the time of diagnosis.

d. Find the probability that a U.S. resident was diagnosed with AIDS and was 25 to 34 years old at the time of diagnosis.

e. Explain in words the difference between parts (c) and (d).