The National Center for Health Statistics, housed within the US. Centers for Disease Control and Prevention (CDC), tracks the number in the US who have health insurance.According to this agency, the uninsured rates for people in the US 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% are ages 18 to 64.

Let

A = American age 65 or older

NA=American under age 65

U = uninsured

1) What is the probability that a randomly selected person in the US is 65 or older?

2) What is the probability that a randomly selected person in the US is under 65 years old?

3) For a random selected person 65 or older, what is the probability that this person is uninsured?

4) For a random selected person under 65, what is the probability that this person is uninsured? This group includes under 18 and 18 to 64

5) Given that the person in the US is uninsured, what is the probability that the person is 65 or older?

In 42 of the 64 years from 1950 through 2014,the S& P 500 finished higher after the first five days of trading (in 2011 there was virtually no change). In 37 out of 42 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 64-year period.

S&P 500's Annual Performance

First week Higher Lower Total

Higher 37 5 42

Lower 11 11 22

Total 48 16 64

a) If a year is selected at random, what is the probability that the S&P 500 finished lower for the year?

b) Given that the S&P fiished lower after the first five days of trading, what is the proability that it finished lower for the year?

c) Are the two events "first week performance" and "annual performance" independent?