Question

consider a political discussion group consisting of 6 democrats, 4 republicans, and 3 independents. suppose that two group members are randomly selected, in succession, to attend a political convention. find the probability of selecting an independent and then a republican. (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total members

Total = 6 + 4 + 3 = 13

Step2: Probability of first Independent

$P(\text{Independent}) = \frac{3}{13}$

Step3: Probability of second Republican

After 1 Independent removed, total = 12, Republicans = 4
$P(\text{Republican}) = \frac{4}{12} = \frac{1}{3}$

Step4: Multiply probabilities

$P = \frac{3}{13} \times \frac{1}{3} = \frac{1}{13}$

Answer:

$\frac{1}{13}$