To determine the correct interpretation of the given data, we will analyze the probability involved.
First, we focus on the problem statement: calculating the probability that a senator is from the Midwest given that the senator is a Republican.
The table provides the following key details:
- The number of Republican senators from the Midwest is 11.
- The total number of Republican senators is 55.
To find the required probability, we calculate the proportion of Republican senators from the Midwest out of all Republican senators. This can be expressed as:
[tex]\[ \text{Probability (Midwest | Republican)} = \frac{\text{Number of Republican senators from the Midwest}}{\text{Total number of Republican senators}} \][/tex]
Using the provided data:
[tex]\[ \text{Probability (Midwest | Republican)} = \frac{11}{55} \][/tex]
This can be simplified:
[tex]\[ \frac{11}{55} = 0.2 \][/tex]
Thus, the probability that a Republican senator is from the Midwest is 0.2 (or 20%).
Given this probability, let's examine the interpretations related to other regions to determine if the Midwest has the highest likelihood:
- Southeast Republicans: [tex]\( \frac{20}{55} \approx 0.3636 \)[/tex]
- Southwest Republicans: [tex]\( \frac{5}{55} \approx 0.0909 \)[/tex]
- West Republicans: [tex]\( \frac{10}{55} \approx 0.1818 \)[/tex]
- Northeast Republicans: [tex]\( \frac{7}{55} \approx 0.1273 \)[/tex]
- Pacific Republicans: [tex]\( \frac{2}{55} \approx 0.0364 \)[/tex]
From the probabilities calculated, we can see that the Southeast has a higher probability of representing a Republican senator (approximately 0.3636 or 36.36%) than the Midwest (0.2 or 20%).
So, the correct interpretation is:
- Option A is incorrect because a Republican senator is more likely to represent the Southeast (36.36%) than the Midwest (20%).
