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
1844 years	50,080	56,405
4564 years	23,768	48,537
6574 years	2,694	15,162
75 years and older	1,247	14,663
Total	77,789	134,767

Case Assignment

1. 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?
2. Identify and discuss the two major categories of probability interpretations, whose adherents possess conflicting views about the fundamental nature of probability.
3. 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.
4. Whatproportionof18-to44-year-oldAmericanshaveneverbeentestedforHIV?Hint:usingthevaluesinthe1844cells,thiswouldbecalculatedasp(NT)/(p(NT)+p(T)),wherepisprobability.Showyourwork.

Please add the references at the end