consider a political discussion group consisting of 4 democrats, 5 republicans, and 5 independents. suppose…
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.)
Answer
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})