The accompanying table shows proportions of adults in...

The accompanying table shows proportions of adults in metropolitan areas, categorized as to whether they are public-radio contributors and whether or not they voted in the last election. $$ \begin{array}{lcc} \hline \text { Voted } & \text { Contributors } & \text { Noncontributors } \\ \hline \text { Yes } & 0.63 & 0.13 \\ \text { No } & 0.14 & 0.10 \\ \hline \end{array} $$ a. What is the probability that a randomly chosen adult from this population voted? b. What is the probability that a randomly chosen adult from this population contributes to public radio? c. What is the probability that a randomly chosen adult from this population did not contribute and did not vote?

The accompanying table shows proportions of adults in metropolitan areas, categorized as to whether they are public-radio contributors and whether or not they voted in the last election.
$$
\begin{array}{lcc}
\hline \text { Voted } & \text { Contributors } & \text { Noncontributors } \\
\hline \text { Yes } & 0.63 & 0.13 \\
\text { No } & 0.14 & 0.10 \\
\hline
\end{array}
$$
a. What is the probability that a randomly chosen adult from this population voted?
b. What is the probability that a randomly chosen adult from this population contributes to public radio?
c. What is the probability that a randomly chosen adult from this population did not contribute and did not vote?

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Key Concepts

Contingency Table

A contingency table is a type of table in statistics that displays the frequency distribution of variables. In this context, it shows the joint distribution of two categorical variables—voting in the election and contributing to public radio—allowing for the examination of relationships between these variables.

Joint Probability

Joint probability refers to the probability of two events happening simultaneously. In a contingency table, each cell represents the joint probability of the occurrence of a specific combination of the two events, such as both voting and contributing, which can be directly read from the table.

Marginal Probability

Marginal probability is the probability of an event occurring irrespective of the outcome of another event. It is calculated by summing the joint probabilities across the rows or columns of a contingency table. For example, to find the probability of voting, one would add the joint probabilities of all cells corresponding to voting.

Addition Rule for Probabilities

The addition rule is used to calculate the probability of the occurrence of at least one of several events. In the context of a contingency table, it involves summing the appropriate joint probabilities to find the overall probability of an event, such as whether an individual voted or contributed.

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