Respuesta :
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.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
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 [tex]P(B) = 0.154[/tex]
1.4% of those 65 and older do not have health insurance.
This means that [tex]P(A|B) = 0.014[/tex]
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
[tex]P(A) = 0.227*0.054 + 0.619*0.128 + 0.154*0.014 = 0.093646[/tex]
Then
[tex]P(B|A) = \frac{0.154*0.014}{0.093646} = 0.023[/tex]
0.023 = 2.3% probability that the person is 65 or older
