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.

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.

Explanation:

Step1: Analyze option A

Calculate the proportion of Republican senators in each region.
For the Midwest: \(\frac{11}{55}\)
For the Southeast: \(\frac{20}{55}\)
Since \(\frac{20}{55}>\frac{11}{55}\), option A is incorrect.

Step2: Analyze option B

There is only 1 independent senator and that senator is from the Northeast. So if a senator is independent, it is certain that the senator is from the Northeast. Option B is correct.

Step3: Analyze option C

In the Southeast, there are 6 Democrats and 20 Republicans. Since \(20 > 6\), given that a senator represents the Southeast, it is likely that the senator is in the Republican Party. Option C is correct.

Answer:

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.