{Exercise 4.45 (Algorithmic)} In an article about investment alternatives, Money
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Question
{Exercise 4.45 (Algorithmic)}
In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 50% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 80% take prescription drugs regularly. For adults age 18 to 64, 45% take prescription drugs regularly. The age 18–64 age group accounts for 86.6% 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?
{Exercise 4.45 (Algorithmic)}
In an article about investment alternatives, Money magazine reported that drug stocks provide a potential for long-term growth, with over 50% of the adult population of the United States taking prescription drugs on a regular basis. For adults age 65 and older, 80% take prescription drugs regularly. For adults age 18 to 64, 45% take prescription drugs regularly. The age 18–64 age group accounts for 86.6% 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:
Given that
P(takes prescription drugs/>=65) = 0.80
P(takes prescription drugs/18-64) = 0.45
P(18-64)= 0.866
P(takes prescription drugs)= 0.80*(1-0.866)+0.45*0.866 = 0.4969
a) P(>=65) = 1-0.866 = 0.134
b) P(>=65/takes prescription drugs)=P(takes perscription drugs/>=65)*P(>=65)/P(takes perscription drugs)
= 0.80*0.134/0.4969 = 0.2157
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