Hello I am having trouble trying to figure out how to do this probability 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).
the only question that I could figure out the answer to is A) which came out to be ".12"
I can't seem to even figure out on how to start solving for the other 3 problems
I have tried writing it out in a tree diagram and a table but I am still stuck
could anyone lend me some help and show me how to solve these problems? any help would be greatly appreciated, thanks in advance!
first split the population into 2 groups
a) over 65
b) under 65, use the data in the last sentence to do that
so for
B) it says to "Compute the probability that a person takes prescription drugs regularly"
- of the over 65, 82% take prescription drugs regularly, so take .82 of a)
- of the under 65, 49% take it regularly, so find .49 of b)
add those two numbers and divide by the total population.
work the others in a similar way.
thanks reiny for the quick reply and i think ive gotten the correct answer for part B came out to be .53
but i try to do the similar things for C) and D) and it's not working.
C) .12 (being >65) x .40(takes 5 or more)
Sure! I can help you solve these probability questions step by step:
A) To compute the probability that a person in the United States is age 65 or older, you need to divide the number of people age 65 or older by the total population of the United States. According to the information provided, there are 34,991,753 people age 65 or older and the total population is 281,421,906. So, the probability is:
Probability = Number of people age 65 or older / Total population
Probability = 34,991,753 / 281,421,906
Probability ≈ 0.1244 (rounded to 2 decimal places)
So, the probability that a person in the United States is age 65 or older is approximately 0.12 or 12%.
Now, let's move on to the other questions:
B) To compute the probability that a person takes prescription drugs regularly, we need to consider the information provided for both age groups. According to the information:
For people age 65 or older:
- 82% take prescription drugs regularly.
For people under age 65:
- 49% take prescription drugs regularly.
To compute the overall probability, we need to weigh these probabilities based on the proportion of each age group in the population. From the information provided, we know that the total population is 281,421,906, and people age 65 or older form 34,991,753 of that population.
Probability = (Proportion of age 65 or older * Probability for age 65 or older) + (Proportion of people under 65 * Probability for people under 65)
Probability = (34,991,753 / 281,421,906) * 0.82 + ((281,421,906 - 34,991,753) / 281,421,906) * 0.49
Probability ≈ 0.6705 (rounded to 2 decimal places)
So, the probability that a person takes prescription drugs regularly is approximately 0.67 or 67%.
Now let's continue with the remaining questions:
C) To compute the probability that a person is age 65 or older and takes five or more prescriptions, we need to consider the information provided for both criteria. According to the information:
For people age 65 or older:
- 40% currently use five or more prescriptions.
To compute the probability, we need to multiply the probability of being age 65 or older by the probability of taking five or more prescriptions, using the values given:
Probability = Probability of being age 65 or older * Probability of taking five or more prescriptions
Probability = 0.1244 * 0.40
Probability ≈ 0.0498 (rounded to 3 decimal places)
So, the probability that a person is age 65 or older and takes five or more prescriptions is approximately 0.050 or 5.0%.
D) Given a person uses five or more prescriptions, we need to compute the probability that the person is age 65 or older. To do this, we can use conditional probability.
Conditional Probability = Probability of being age 65 or older and using five or more prescriptions / Probability of using five or more prescriptions
From the previous question, we found that the probability of being age 65 or older and using five or more prescriptions is approximately 0.050. Now, we need to find the probability of using five or more prescriptions.
To do this, we need to consider the information provided for both age groups:
For people age 65 or older:
- 40% currently use five or more prescriptions.
For people under age 65:
- 28% use five or more prescriptions.
From this, we can calculate the overall probability of using five or more prescriptions:
Probability of using five or more prescriptions = (Proportion of age 65 or older * Probability for age 65 or older) + (Proportion of people under 65 * Probability for people under 65)
Probability of using five or more prescriptions = (34,991,753 / 281,421,906) * 0.40 + ((281,421,906 - 34,991,753) / 281,421,906) * 0.28
You can calculate the probability of using five or more prescriptions using the values provided. Once you have that value, simply divide the probability of being age 65 or older and using five or more prescriptions by the probability of using five or more prescriptions to calculate the conditional probability.
I hope this helps you solve the remaining questions! Let me know if you have any further questions.