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The table shows differences in political ideology, by education, for a random sample of voters. Use the data to solve the problem.

\begin{tabular}{|l|c|c|c|}
\hline & Liberal & Moderate & Conservative \\
\hline
High School only & 16 & 15 & 17 \\
\hline
College & 22 & 10 & 20 \\
\hline
\end{tabular}

Find the probability that a randomly selected person from this group is conservative, given they have only a high school education.

[tex]\[
\boxed{\text{Type an integer or a simplified fraction.}}
\][/tex]

Sagot :

GinnyAnswer
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]
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