To solve the given problem, follow these steps:
1. Total Respondents: We start by noting that the total number of respondents is 250.
2. Liberal Respondents: We see that among these 250 respondents, 60 identify as Liberal.
3. Probability Calculation:
- The probability of a randomly selected person identifying as Liberal is found by dividing the number of Liberal respondents by the total number of respondents. This is calculated as:
[tex]\[
\text{Probability of identifying as Liberal} = \frac{\text{Number of Liberals}}{\text{Total Respondents}} = \frac{60}{250}
\][/tex]
4. Simplifying the fraction:
- Converting [tex]\( \frac{60}{250} \)[/tex] into a decimal form we get:
[tex]\[
\frac{60}{250} = 0.24
\][/tex]
This gives us the first result:
- The probability of a randomly selected person identifying as Liberal is 0.24.
Next, let's find the probability of a randomly selected respondent identifying as Liberal and having a college degree.
5. Liberal with College Degree: From the table, 42 respondents are Liberal and have a college degree.
6. Probability Calculation:
- The probability that a randomly selected person identifies as Liberal and has a college degree is calculated as:
[tex]\[
\text{Probability of identifying as Liberal and having a college degree} = \frac{\text{Number of Liberals with College Degree}}{\text{Total Respondents}} = \frac{42}{250}
\][/tex]
7. Simplifying the fraction:
- Converting [tex]\( \frac{42}{250} \)[/tex] into a decimal form we get:
[tex]\[
\frac{42}{250} = 0.168
\][/tex]
This gives us the second result:
- The probability of a randomly selected person identifying as Liberal and having a college degree is 0.168.
### Summary
- The probability of a randomly selected person identifying as Liberal is 0.24.
- The probability of a randomly selected person identifying as Liberal and having a college degree is 0.168.
