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Answer:
a) 15.4% probability that a randomly selected person in this country is 65 or older
b) 0.023 = 2.3% probability that the person is 65 or older
Step-by-step explanation:
To solve b), i will use the Bayes Theorem.
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
(a) What is the probability that a randomly selected person in this country is 65 or older?
22.7% of people in the county are under age 18
61.9% are ages 18–64
p% are 65 or older.
The sum of those is 100%. So
22.7 + 61.9 + p = 100
p = 100 - (22.7+61.9)
p = 15.4
15.4% probability that a randomly selected person in this country is 65 or older.
(b) Given that a person in this country is uninsured, what is the probability that the person is 65 or older?
Event A: Uninsured
Event B: 65 or older.
15.4% probability that a randomly selected person in this country is 65 or older.
This means that
1.4% of those 65 and older do not have health insurance.
This means that
Probability of not having insurance.
22.7% are under 18. Of those, 5.4% do not have insurance.
61.9% are aged 18-64. Of those, 12.8% do not have insurance.
15.4% are 65 or over. Of those, 1.4% do not have health insurance. So
Then
0.023 = 2.3% probability that the person is 65 or older