Hello I am having trouble trying to figure out how to do the last 2 questions in this word problem
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 age 65 take prescriptions regularly, with 37% taking three or more prescriptions regularly and 28% using five or more prescriptions (Money, September 2001). The U.S. Census Bureau reports that of the 281,421,906 people in the United States, 34,991,753 are age 65 years and older (U.S. Census Bureau, Census 2000).
questions:
(A) Compute the probability that a person in the United States is age 65 or older (to 2 decimals).
(B) Compute the probability that a person takes prescription drugs regularly (to 2 decimals).
(C) Compute the probability that a person is age 65 or older and takes five or more prescriptions (to 3 decimals).
(D) Given a person uses five or more prescriptions, compute the probability that the person is age 65 or older (to 2 decimals).
correct answers for
(A)".12"
(B)".53"
I don't know how to start solving for question (C) and (D) and I have tried using similar techniques in solving for (A) and (B)
any help is appreciated, thanks in advance!
Answered above
To solve questions (C) and (D), we will need to use the concept of conditional probability, which involves finding the probability of an event given that another event has already occurred.
Let's break down each question step by step:
(C) Compute the probability that a person is age 65 or older and takes five or more prescriptions (to 3 decimals).
To find this probability, we need to calculate the ratio of people who are age 65 or older and take five or more prescriptions to the total population.
1. Calculate the number of people age 65 or older who take five or more prescriptions:
- Given that 34,991,753 people are age 65 or older, we can calculate the number of individuals taking five or more prescriptions by multiplying 40% with this population.
- Number of people age 65 or older taking five or more prescriptions = 34,991,753 * 0.40 = X (where X is the result)
2. Calculate the probability by dividing the above number by the total population of the United States (281,421,906):
- Probability = X / 281,421,906
- Round the answer to three decimal places.
(D) Given a person uses five or more prescriptions, compute the probability that the person is age 65 or older (to 2 decimals).
To find this probability, we need to calculate the ratio of people who are age 65 or older and take five or more prescriptions to the total number of people who take five or more prescriptions.
1. Calculate the number of people who take five or more prescriptions:
- Given that 40% of people age 65 or older and 28% of people under age 65 take five or more prescriptions, we can calculate the total number of individuals taking five or more prescriptions.
- Number of people taking five or more prescriptions = (34,991,753 * 0.40) + (281,421,906 * 0.28) = Y (where Y is the result)
2. Calculate the probability by dividing the number of age 65 or older individuals taking five or more prescriptions by the total number of people who take five or more prescriptions:
- Probability = (34,991,753 * 0.40) / Y
- Round the answer to two decimal places.
By following these steps, you should be able to solve questions (C) and (D) in the word problem.