Question

consider a political discussion group consisting of 4 democrats, 7 republicans, and 2 independents. suppose that two group members are randomly selected, in succession, to attend a political convention. find the probability of selecting two independents.
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total members

Total members = 4 + 7+ 2 = 13.

Step2: Calculate probability of first - independent selection

Probability of selecting first independent = $\frac{2}{13}$.

Step3: Calculate probability of second - independent selection

After one independent is selected, there is 1 independent left and 12 members left. So probability of selecting second independent = $\frac{1}{12}$.

Step4: Calculate probability of both events

Since these are independent events (successive selection), we multiply the probabilities. Probability of selecting two independents = $\frac{2}{13}\times\frac{1}{12}=\frac{2}{156}=\frac{1}{78}$.

Answer:

$\frac{1}{78}$