Question

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

$$\begin{tabular}{|c|c|c|} \\hline & high school only & college \\\\ \\hline liberal & 10 & 18 \\\\ \\hline moderate & 24 & 20 \\\\ \\hline conservative & 10 & 13 \\\\ \\hline \\end{tabular}$$

\

1. find the probability that a randomly selected person from this group is conservative, given they have attended college. \
2. find the probability that a randomly selected person from this group is conservative, given they have attended college. \

(type an integer or a simplified fraction)

Explanation:

Step1: Identify college-attended totals

First, sum all voters who attended college:
$\text{Total College Voters} = 18 + 20 + 13 = 51$

Step2: Identify college conservative voters

Number of conservative college voters:
$\text{College Conservative} = 13$

Step3: Calculate conditional probability

Use conditional probability formula $P(A|B)=\frac{P(A\cap B)}{P(B)}$, here it is $\frac{\text{College Conservative}}{\text{Total College Voters}}$
$\text{Probability} = \frac{13}{51}$

Answer:

$\frac{13}{51}$