Refer to Table 3.10. What is the conditional probability of...

Refer to Table 3.10. What is the conditional probability of "high income," given "never"? $$ \begin{aligned} &\text { Table 3.10 Probabilities for Television Viewing and Income }\\ &\begin{array}{|lcccc|} \hline \text { Viewing FrequenCY } & \text { High INCOMe } & \text { Middle INcome } & \text { Low Income } & \text { Totals } \\ \hline \text { Regular } & 0.10 & 0.15 & 0.05 & 0.30 \\ \text { Occasional } & 0.10 & 0.20 & 0.10 & 0.40 \\ \text { Never } & 0.05 & 0.05 & 0.20 & 0.30 \\ \text { Totals } & 0.25 & 0.40 & 0.35 & 1.00 \\ \hline \end{array} \end{aligned} $$

Refer to Table 3.10.
What is the conditional probability of "high income," given "never"?
$$
\begin{aligned}
&\text { Table 3.10 Probabilities for Television Viewing and Income }\\
&\begin{array}{|lcccc|}
\hline \text { Viewing FrequenCY } & \text { High INCOMe } & \text { Middle INcome } & \text { Low Income } & \text { Totals } \\
\hline \text { Regular } & 0.10 & 0.15 & 0.05 & 0.30 \\
\text { Occasional } & 0.10 & 0.20 & 0.10 & 0.40 \\
\text { Never } & 0.05 & 0.05 & 0.20 & 0.30 \\
\text { Totals } & 0.25 & 0.40 & 0.35 & 1.00 \\
\hline
\end{array}
\end{aligned}
$$

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Key Concepts

Conditional Probability

This concept refers to the probability of an event occurring given that another event has already occurred. It is calculated by dividing the joint probability of the two events by the probability of the given condition, and it helps in understanding how the occurrence of one event affects the likelihood of another.

Joint Probability

This is the probability of two events occurring together. In the context of a contingency table, the joint probability is found at the intersection of the row and column corresponding to the two events of interest. It is a fundamental building block for calculating conditional probabilities.

Marginal Probability

Marginal probability refers to the probability of a single event occurring irrespective of the occurrence of other events. It is typically obtained by summing the joint probabilities across the corresponding row or column in a contingency table and serves as the denominator in the calculation of conditional probabilities.

Contingency Table

A contingency table is a tabular representation that displays the joint frequency or probability distribution of variables. It organizes data to illustrate the relationship between different categorical events, enabling the computation of joint, marginal, and conditional probabilities.

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