Consider a political discussion group consisting of 9 Democrats, 6 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 Democrats.
(Type an integer or a simplified fraction.)
Answer
Final Answer: The probability of selecting two Democrats is \(\boxed{\frac{9}{34}}\).
Step 1 ：The total number of people in the group is 9 (Democrats) + 6 (Republicans) + 2 (Independents) = 17.
Step 2 ：We are selecting 2 people from this group. The probability of selecting a Democrat on the first draw is \(\frac{9}{17}\).
Step 3 ：If a Democrat is selected on the first draw, there are now 8 Democrats left and the total number of people in the group is 16. So, the probability of selecting a Democrat on the second draw, given that a Democrat was selected on the first draw, is \(\frac{8}{16}\).
Step 4 ：The probability of both events happening is the product of the probabilities of each event.
Step 5 ：Final Answer: The probability of selecting two Democrats is \(\boxed{\frac{9}{34}}\).
