Using data from the 2000 census, a random sample of 348 U.S. residents aged 18 and older was selected.

Suppose that each student in a sample had been categorized with respect to political views, marijuana usage, and religious preference, with the categories of this latter factor being Protestant, Catholic, and other. The data could be displayed in three different two-way tables, one corresponding to each category of the third factor.

Use the two-way table of data from another student survey to answer the following question.
Like Aerobic Exercise Like Weight Lifting Yes No Total Yes 7 14 21 No 12 7 19 Total 19 21 40
Find the joint relative frequency of students surveyed who like aerobics exercise but dislike weight lifting.

You randomly survey students in your school about whether they have a pet. You display your results in the two-way table. How many female students took the survey?
$\begin{array}{}& & Pet\\ Gender& Male& 33& 8\\ & Female& 35& 11\end{array}$

Researchers carried our a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked if good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Find ${\displaystyle (A\cup D)}$ using the following table.

In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
$\begin{array}{lcc}& \text{Class}\text{Survived }& \begin{array}{cccc}& \text{ First }& \text{ Second }& \text{ Third }\\ \text{ Yes }& 197& 94& 151\\ \text{ No }& 122& 167& 476\end{array}\end{array}$
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P(not a passenger in first class or survived).

Bayes' Theorem is given by $P(A|B)=\frac{P(B|A)\cdot P(A)}{P(B)}$. Use a two-way table to write an example of Bayes' Theorem.