Let's break down the problem systematically and answer each question step by step based on the data provided.

Data Summary:

Part a: What percent of survey respondents identified themselves as Republicans?

This is a marginal probability: $P(\text{Republican}) = \frac{\text{Number of Republicans}}{\text{Total respondents}} = \frac{186}{651}.$

Calculating: $P(\text{Republican}) = \frac{186}{651} \approx 28.6\%.$

Part b: What percent of survey respondents thought the economy was getting worse and were Republicans?

This is a joint probability: $P(\text{Republican and Worse}) = \frac{\text{Number of Republicans who thought the economy was getting worse}}{\text{Total respondents}} = \frac{44}{651}.$

Calculating: $P(\text{Republican and Worse}) = \frac{44}{651} \approx 6.8\%.$

Part c: What percent of Republicans thought the economy was getting worse?

This is a conditional probability: $P(\text{Worse | Republican}) = \frac{\text{Number of Republicans who thought the economy was getting worse}}{\text{Total Republicans}} = \frac{44}{186}.$

Calculating: $P(\text{Worse | Republican}) = \frac{44}{186} \approx 23.7\%.$

Final Answers:

• a) $28.6\%$
• b) $6.8\%$
• c) $23.7\%$

Let me know if you'd like a detailed explanation for any part or clarification!

Follow-up Questions:

1. What is the percentage of Democrats who thought the economy was "about the same"?
2. What is the probability that a respondent was unaffiliated and thought the economy was "getting better"?
3. How many total respondents thought the economy was "getting worse" regardless of party affiliation?
4. What percent of all respondents thought the economy was "about the same"?
5. What is the conditional probability that a Democrat thought the economy was "getting worse"?

Tip: Always verify if probabilities sum to $100\%$ across all categories as a quick check for accuracy.