In an article about investment alternatives, Money magazine reported that drug s

Question

In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 53% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 81% take prescription drugs regularly. For adults age 18 to 64, 45% take prescription drugs regularly. The age 18–64 age group accounts for 85.7% of the adult population (Statistical Abstract of the United States, 2008).

Round your answers to 4 decimal places.

a. What is the probability that a randomly selected adult is 65 or older?

b. Given an adult takes prescription drugs regularly, what is the probability that the adult is 65 or older?

Explanation / Answer

Solution:

a) Adults are made up of those 18-64 and those 65+
Thus,
P(an adult is 65+) = 1 - P(an adult is 18-64) =
= 1 - 0.857 = 0.143 or 14.3%

b) For this problem, we need to figure the
P(adult is 65 or older | the adult takes drugs) = P(adult 65 or older and takes drugs)/P(adult takes drugs)

The numerator equals 0.143 * 0.81
The denominator equals 0.143 * 0.81 + 0.857 * 0.45 (including those 65+ and those 18-64 taking drugs)

Then, P(adult is 65 or older | the adult takes drugs) =
0.143 * 0.81/(0.143 * 0.81 + 0.857 * 0.45 ) = 0.23097631 = 0.231 = 23.1%.

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