Question

consider a political discussion group consisting of 10 democrats, 5 republicans, and 4 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.)

Explanation:

Step1: Calculate total number of members

Total members = \(10 + 5+4=19\)

Step2: Calculate probability of first - Democrat selection

Probability of selecting first Democrat \(P(D_1)=\frac{10}{19}\)

Step3: Calculate probability of second - Democrat selection

After one Democrat is selected, there are \(9\) Democrats left and \(18\) total members left. Probability of selecting second Democrat \(P(D_2|D_1)=\frac{9}{18}\)

Step4: Use multiplication rule for dependent events

By the formula \(P(D_1\cap D_2)=P(D_1)\times P(D_2|D_1)\)

$$
LATEXBLOCK0
$$

Answer:

\(\frac{5}{19}\)