Question

consider a political discussion group consisting of 9 democrats, 7 republicans, and 4 independents. suppose that two group members are randomly selected, in succession, to attend a political convention. find the probability of selecting a democrat and then a republican. (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total members

The total number of members in the group is $9 + 7+4=20$.

Step2: Calculate probability of selecting a Democrat first

The probability of selecting a Democrat first is $\frac{9}{20}$ since there are 9 Democrats out of 20 total members.

Step3: Calculate probability of selecting a Republican second

After one Democrat is selected, there are 19 members left. The probability of selecting a Republican second is $\frac{7}{19}$ since there are 7 Republicans among the remaining 19 members.

Step4: Calculate combined probability

The probability of both events happening (selecting a Democrat and then a Republican) is the product of the two - probabilities. So $P=\frac{9}{20}\times\frac{7}{19}=\frac{63}{380}$.

Answer:

$\frac{63}{380}$