Step-by-Step Solution:
1. Identify the relevant data from the table:
- Number of high school only liberals: 16
- Number of high school only moderates: 15
- Number of high school only conservatives: 17
2. Calculate the total number of high school only voters:
[tex]\[
\text{Total number of high school only voters} = 16 + 15 + 17
\][/tex]
Adding these values together gives:
[tex]\[
16 + 15 + 17 = 48
\][/tex]
3. Identify the number of conservative voters with only a high school education:
The number is given as 17.
4. Calculate the probability that a randomly selected person from those with only a high school education is conservative:
[tex]\[
\text{Probability (Conservative | High School only)} = \frac{\text{Number of high school only conservatives}}{\text{Total number of high school only voters}}
\][/tex]
Substituting in the values we obtained:
[tex]\[
\text{Probability (Conservative | High School only)} = \frac{17}{48}
\][/tex]
5. Convert the fraction to a simplified fraction or decimal (if necessary for explanation purposes, though the question specifies a fraction):
The fraction [tex]\(\frac{17}{48}\)[/tex] is already in its simplest form.
6. Result:
The probability that a randomly selected person from this group is conservative, given they have only a high school education, is:
[tex]\[
\boxed{\frac{17}{48}}
\][/tex]
