In an article about investment growth, Money magazine reported that drug stocks
ID: 3070098 • Letter: I
Question
In an article about investment growth, Money magazine reported that drug stocks show powerful long-term trends and offer investors unparalleled potential for strong and steady gains. The federal Health Care Financing Administration supports this conclusion through its forecast that annual prescription drug expenditures will reach $366 billion by 2010, up from $117 billion in 2000. Many individuals age 65 and older rely heavily on prescription drugs. For this group, 82% take prescription drugs regularly, 55% take three or more prescriptions regularly, and 40% currently use five or more prescriptions. In contrast, 49% of people under the age of 65 take prescriptions regularly, with 17% taking three or more prescriptions regularly and 28% using five or more prescriptions. The U.S. Census Bureau reports that the probability that a person in the United States is age 65 or older is 12%.
a. Compute the probability that a person takes prescription drugs regularly.
b. Compute the probability that a person is age 65 or older and takes five or more prescriptions.
c. Given a person uses five or more prescriptions, compute the probability that the person is age 65 or older.
Explanation / Answer
a)probability that a person takes prescription drugs regularly
=P(below 65 and takes prescription drugs regularly)+P(above 65 and takes prescription drugs regularly)
=(1-0.12)*0.49+0.12*0.82=0.5296
b)
probability that a person is age 65 or older and takes five or more prescriptions =0.12*0.40=0.048
c) P(5 or more prescriptions)=P(below 65 and5 or more prescriptions)+P(above 65 and 5 or more prescriptions) =(1-0.12)*0.28+0.12*0.40=0.2944
henc e P(above 65 |5 or more prescriptions)
=P(above 65 and 5 or more prescriptions)/ P(5 or more prescriptions)=0.12*0.4/0.2944=0.163043
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