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?

P(uninsured) = p(those not up to 18) * p(those uninsured or under 18) + p(those age 18-64) * p(uninsured or under 18) + p(being 64plus) x P(uninsured or 64 plus)

= 0.228 x 0.051 + 0.614 x 0.124 + 0.158 x 0.011

= 0.011628 + 0.076136 + 0.001738

=0.089502

P(65 of older|uninsured) = p(64+) x P(uninsured or 64 plus)

= 0.157 x 0.011/0.089502

= 0.001738/0.089502

= 0.01942

andromache andromache · Answer 2 · 2022-02-14T05:05:01+01:00

a. The probability that a randomly selected person in the United States is 65 or older is 0.158

b. In the case when the person is an uninsured American so the probability is 0.01942

Calculation of probabilities:

a.

Since

Probability of under age = 22.8% = 0.228

And,

Probability of those from age 18 to 64 = 61.4% = 0.614

So, the probabilities of 65 or older is

= 1 - 0.228-0.614

= 0.158

b.

Now

P(uninsured) = p(those not up to 18) × p(those uninsured or under 18) + p(those age 18-64) × p(uninsured or under 18) + p(being 64plus) × P(uninsured or 64 plus)

= 0.228 × 0.051 + 0.614 × 0.124 + 0.158 × 0.011

= 0.011628 + 0.076136 + 0.001738

=0.089502

So,

P(65 of older|uninsured) = p(64+) × P(uninsured or 64 plus)

= 0.157 × 0.011 ÷ 0.089502

= 0.001738 ÷ 0.089502

= 0.01942

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