Question

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

	high school only	college
moderate	25	10
conservative	22	9

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

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

( type an integer or a simplified fraction. )

Explanation:

Step1: Calculate total high school respondents

Add the counts for liberal, moderate, and conservative high school-only voters.
$23 + 25 + 22 = 70$

Step2: Identify moderate high school respondents

Extract the count of moderate high school-only voters from the table.
$\text{Count} = 25$

Step3: Compute conditional probability

Divide the number of moderate high school-only voters by the total number of high school-only voters, then simplify the fraction.
$\frac{25}{70} = \frac{5}{14}$

Answer:

$\frac{5}{14}$