Leon is interested in the relationships among geographic region and political affiliation. Leon collected data about the political parties of US senators at that time and the regions of the US that they represent. His results are in the table below.
\begin{tabular}{lllll}
Region & Democrats & Republicans & Independents & Total \
\hline Southeast & 6 & 20 & 0 & 26 \
Southwest & 1 & 5 & 0 & 6 \
West & 8 & 10 & 0 & 18 \
Midwest & 13 & 11 & 0 & 24 \
Northeast & 14 & 7 & 1 & 22 \
Pacific & 2 & 2 & 0 & 4 \
Total & 44 & 55 & 1 & 100
\end{tabular}

Which of the following interpretations are correct?
Choose all answers that apply:

A Given that a senator was in the Republican Party, the senator was more likely to represent the midwest than any other region.

B Given that a senator is an Independent, it is certain that the senator represented the northeast.

C Given that a senator represents the southeast, it is likely that the senator is in the Republican Party.

Question

Leon is interested in the relationships among geographic region and political affiliation. Leon collected data about the political parties of US senators at that time and the regions of the US that they represent. His results are in the table below.
\begin{tabular}{lllll} 
Region & Democrats & Republicans & Independents & Total \
\hline Southeast & 6 & 20 & 0 & 26 \
Southwest & 1 & 5 & 0 & 6 \
West & 8 & 10 & 0 & 18 \
Midwest & 13 & 11 & 0 & 24 \
Northeast & 14 & 7 & 1 & 22 \
Pacific & 2 & 2 & 0 & 4 \
Total & 44 & 55 & 1 & 100
\end{tabular}

Which of the following interpretations are correct?
Choose all answers that apply:

A Given that a senator was in the Republican Party, the senator was more likely to represent the midwest than any other region.

B Given that a senator is an Independent, it is certain that the senator represented the northeast.

C Given that a senator represents the southeast, it is likely that the senator is in the Republican Party.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the correctness of statement A, we need to compare the number of Republican senators in the Midwest to the number of Republican senators in other regions. ‖ ‖ step 2 ⋮ According to the table, there are 11 Republican senators in the Midwest. ‖ ‖ step 3 ⋮ The region with the highest number of Republican senators is the Southeast, with 20 Republican senators. ‖ ‖ step 4 ⋮ Since 20 (Southeast) is greater than 11 (Midwest), statement A is incorrect. ‖ ‖ step 5 ⋮ To verify statement B, we look at the number of Independent senators in each region. ‖ ‖ step 6 ⋮ There is only 1 Independent senator, and they represent the Northeast. ‖ ‖ step 7 ⋮ Therefore, statement B is correct because it is certain that the Independent senator represented the Northeast. ‖ ‖ step 8 ⋮ To assess statement C, we examine the likelihood of a senator from the Southeast being a Republican. ‖ ‖ step 9 ⋮ There are 26 senators in total from the Southeast, with 20 being Republicans. ‖ ‖ step 10 ⋮ The probability that a senator from the Southeast is a Republican is $\frac{20}{26}$, which is approximately 0.77. ‖ ‖ step 11 ⋮ Since this probability is high, statement C is correct. ‖ ∻1 Answer∻ ***B, C*** ∻Key Concept∻ ⚹Conditional Probability and Certain Events⚹ ∻Explanation∻ ⚹To determine the correctness of the statements, we used the concepts of conditional probability for statements A and C, and the concept of certainty for statement B. Conditional probability assesses the likelihood of an event given that another event has occurred, while certainty implies that an event will definitely occur.⚹◊What is the probability that a randomly selected senator represents the West region?⍭ Generate me a similar question◊

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