Question

consider a political discussion group consisting of 4 democrats, 5 republicans, and 5 independents. suppose that two group - members are randomly selected, in succession, to speak. find the probability of selecting two democrats. (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of people

The total number of people in the group is \(4 + 5+5=14\).

Step2: Calculate probability of first - selection

The probability of selecting a Democrat on the first draw is \(\frac{4}{14}\).

Step3: Calculate probability of second - selection

After one Democrat is selected, there are 3 Democrats left and 13 people left in total. So the probability of selecting a Democrat on the second draw given that a Democrat was selected on the first draw is \(\frac{3}{13}\).

Step4: Calculate the joint - probability

By the multiplication rule for independent events (in the context of sequential selection without replacement), the probability of selecting two Democrats is \(\frac{4}{14}\times\frac{3}{13}=\frac{12}{182}=\frac{6}{91}\).

Answer:

\(\frac{6}{91}\)