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 below
The answer is- you mom! OOOOOOHHHHH!!!!
For question (C), you need to find the probability that a person is age 65 or older and takes five or more prescriptions. To do this, you will need to use the information given in the word problem.
The word problem states that 40% of individuals age 65 and older currently use five or more prescriptions. From the U.S. Census Bureau data, we know that there are 34,991,753 people age 65 years and older in the United States.
To calculate the probability, you need to divide the number of people who are age 65 or older and take five or more prescriptions by the total population of the United States. The calculation would look like this:
Probability = (Number of people age 65 or older and taking five or more prescriptions) / (Total population of the United States)
Number of people age 65 or older and taking five or more prescriptions = 40% of 34,991,753
Total population of the United States = 281,421,906
Now you can substitute these values into the equation and solve:
Probability = (0.40 * 34,991,753) / 281,421,906
Evaluate this expression to get the probability. Round your answer to 3 decimal places as requested in the question.
For question (D), you need to find the probability that a person is age 65 or older given that they use five or more prescriptions. To find this probability, you will need to use conditional probability.
The conditional probability formula is P(A | B) = P(A and B) / P(B), where P(A | B) represents the probability of A given B, P(A and B) represents the probability of both A and B occurring, and P(B) represents the probability of B occurring.
In question (D), A is the event of a person being age 65 or older, and B is the event of a person using five or more prescriptions.
You have already calculated the probability of a person being age 65 or older and taking five or more prescriptions in the previous question (C) as P(A and B). Now, you need to find the probability of a person using five or more prescriptions, which is P(B).
To calculate P(B), you can use the information provided in the word problem. It states that 55% of individuals age 65 and older take three or more prescriptions regularly, and 40% currently use five or more prescriptions. So, P(B) is 40%.
Now, you can substitute these values into the conditional probability formula:
P(A | B) = P(A and B) / P(B)
P(A | B) = (Probability of a person being age 65 or older and taking five or more prescriptions) / (Probability of a person taking five or more prescriptions)
You can use the values calculated in question (C) and the given probability of people age 65 and older taking five or more prescriptions to find the answer to question (D). Round your answer to 2 decimal places as requested in the question.