In a certain small town, 65% of the households subscribe to the daily paper, 37% subscribe to the weekly local paper, and 25% subscribe to both papers

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses.
$\begin{array}{cccc}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ Almost no chance }& 96& 98& 194\\ \text{ Some chance but }\text{ probably not }& 426& 286& 712\\ \text{ A 50-50 chance }& 696& 720& 1416\\ \text{ A good chance }& 663& 758& 1421\\ \text{ Almost certain }& 486& 597& 1083\\ \text{ Total }& 2367& 2459& 4826\end{array}$
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find $P(C\mid M)$. Interpret this value in context.

The two-way table summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level.

$\text{Grade}\text{Eat in cafeteria}\begin{array}{lrrrrr}& 9\mathrm{th}& 10\mathrm{th}& 11\mathrm{th}& 12\mathrm{th}& \text{ Total }\\ \text{ Yes }& 130& 175& 122& 68& 495\\ \text{ No }& 18& 34& 88& 170& 310\\ \text{ Total }& 148& 209& 210& 238& 805\end{array}$

If you choose a student at random who eats regularly in the cafeteria, what is the probability that the student is a 10th-grader?

Here are the row and column totals for a two-way table with two rows and two columns:$\begin{array}{llr}a& b& 50\\ c& d& 50\\ 60& 40& 100\end{array}$ Find two different sets of counts a, b, c, and d for the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

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. With pijk = P(political category i, marijuana category j, and religious category k), the null hypothesis of independence of all three factors states that $p_{ijk}=p_i..p_j..p_k$
Let nijk denote the observed frequency in cell (i, j, k). Show how to estimate the expected cell counts assuming that H0 is true (${\hat{e}}_{ijk}=n{\hat{p}}_{ijk}$, so the ${\hat{p}}_{ijk}$’s must be determined). Then use the general rule of thumb to determine the number of degrees of freedom for the chi-squared statistic.