## National Health Interview

Suppose that a 2012 National Health Interview Survey gives the number of adults in the United States which gives the number of adults in the United States (reported in thousands) classified by their age group, and whether or not respondents have ever been tested for HIV. Here are the data:
Age Group
Tested
Never Tested
18–44 years
50,080
56,405
45–64 years
23,768
48,537
65–74 years
2,694
15,162
75 years and older
1,247
14,663
Total
77,789
134,767
Discuss probability. What is its history? What is the theory of probability? How is it calculated? What are the advantages and disadvantages of using this technique?
1. Identify and discuss the two major categories of probability interpretations, whose adherents possess conflicting views about the fundamental nature of probability.
2. Based on this survey, what is the probability that a randomly selected American adult has never been tested? Show your work. Hint: using the data in the two total rows, this would be calculated as p (NT) /( p (NT) + p (T)), where p is probability.
3. What proportion of 18- to 44-year-old Americans have never been tested for HIV? Hint: using the values in the 18–44 cells, this would be calculated as p (NT) / ( p (NT) + p (T)), where p is probability. Show your work.