Data Analysis One hundred college students were interviewed...

Data Analysis One hundred college students were interviewed to determine their political party affiliations and whether they favored a balanced budget amendment to the Constitution. The results of the study are listed in the table, where $D$ represents Democrat and $R$ represents Republican. $$ \begin{array}{|c|c|c|c|}\hline & {D} & {R} & {\text { Total }} \\ \hline \text { Favor } & {23} & {32} & {55} \\ {\text { Oppose }} & {25} & {9} & {34} \\ {\text { Unsure }} & {7} & {4} & {11} \\ {\text { Total }} & {55} & {45} & {100} \\ \hline\end{array} $$ A person is selected at random from the sample. Find the probability that the person selected is (a) a person who doesn't favor the amendment, (b) a Republican, (c) a Democrat who favors the amendment.

Data Analysis One hundred college students were interviewed to determine their political party affiliations
and whether they favored a balanced budget amendment to the Constitution. The results of the study are listed in the table, where $D$ represents Democrat and $R$ represents Republican.
$$
\begin{array}{|c|c|c|c|}\hline & {D} & {R} & {\text { Total }} \\ \hline \text { Favor } & {23} & {32} & {55} \\ {\text { Oppose }} & {25} & {9} & {34} \\ {\text { Unsure }} & {7} & {4} & {11} \\ {\text { Total }} & {55} & {45} & {100} \\ \hline\end{array}
$$
A person is selected at random from the sample. Find the probability that the person selected is (a) a person who doesn't favor the amendment, (b) a Republican, (c) a Democrat who favors the amendment.

Key Concepts

Probability

Probability is the measure of the likelihood of an event occurring, calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space. It forms the basis of interpreting data in statistics by quantifying uncertainty.

Contingency Table Analysis

A contingency table is a structured format for displaying the frequencies of different combinations of categorical variables. It is essential for organizing data, allowing for easy computation of both marginal and joint probabilities, and for identifying relationships between variables.

Relative Frequency Interpretation

Relative frequency is the ratio of the number of times an event occurs to the total number of trials or observations. This concept is used to estimate probabilities empirically and is especially useful when direct analytical probabilities are not available.

Joint and Marginal Probability

Joint probability refers to the probability of two events occurring simultaneously, while marginal probability is the probability of a single event occurring without consideration of other variables. Understanding both is crucial for analyzing interdependent events in data sets.

Complement Rule in Probability

The complement rule states that the probability of an event not occurring is equal to one minus the probability of the event occurring. This rule is particularly useful in situations where calculating the probability of the complementary event is more straightforward than calculating the event itself.

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