Question

The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018 are as follows: 5.1% of those under the age of 18, 12.4% of those ages 18–64, and 1.1% of those 65 and older do not have health insurance (CDC website). Approximately 22.8% of Americans are under age 18, and 61.4% of Americans are ages 18–64.

a. What is the probability that a randomly selected person in the United States is 65 or older?

b.Given that the person is an uninsured American, what is the probability that the person is 65 or older?

Answer 1

a)

probability that a randomly selected person in the United States is 65 or older

1-P( under the age of 18 )-P( ages 18–64 )

=1-0.228-0.614

=0.158

b)

P(uninsured)=P(under 18)*P(uninsured|under 18)+P(18-64)*P(uninsured|under 18)+P(64+)*P(uninsured|64+)

=0.228*0.051+0.614*0.124+0.158*0.011 =0.089502

P(65 or older |uninsured) =P(64+)*P(uninsured|64+)/P(uninsured)=0.158*0.011/0.089502

=0.019419