In the 2012 presidential clection, exit polls from the...

In the 2012 presidential clection, exit polls from the critical state of Ohio provided the following results: $$\begin{array}{lcc}\text { Total } & \text { Obama } & \text { Romney } \\\text { No college degree }(60 \%) & 52 \% & 45 \% \\\text { Collcge graduate }(40\%) & 47 \% & 51 \%\end{array}$$ What is the probability a randomly selected respondent voted for Obama?

In the 2012 presidential clection, exit polls from the critical state of Ohio provided the following results:
$$\begin{array}{lcc}\text { Total } & \text { Obama } & \text { Romney } \\\text { No college degree }(60 \%) & 52 \% & 45 \% \\\text { Collcge graduate }(40\%) & 47 \% & 51 \%\end{array}$$
What is the probability a randomly selected respondent voted for Obama?

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Key Concepts

Weighted Average

A weighted average takes into account the relative importance, or weight, of each subgroup when combining their probabilities. In election exit poll analysis, the responses from different demographic groups are averaged based on their proportion in the total population, ensuring that each group's influence is appropriately reflected in the final result.

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another event has already occurred. In the context of exit polls, it refers to the probability of a respondent voting for a candidate, given a specific characteristic (such as having a college degree or not). This concept is crucial when considering how different factors influence the overall outcome.

Law of Total Probability

This principle allows us to compute the overall probability of an event by breaking it down into several distinct groups or conditions and then summing the weighted probabilities for each group. In contexts like exit polls, it is used to combine the voting probabilities across different demographic segments to determine an overall voting probability.

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