Question

consider a political discussion group consisting of 7 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 republican and then an independent.
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total members

The total number of members in the group is $7 + 7+4=18$.

Step2: Calculate probability of first - selecting a Republican

The probability of selecting a Republican first is $\frac{7}{18}$ since there are 7 Republicans out of 18 total members.

Step3: Calculate probability of then selecting an Independent

After one member is selected (a Republican), there are 17 members left. The probability of selecting an Independent next is $\frac{4}{17}$ since there are 4 Independents out of the remaining 17 members.

Step4: Calculate the combined probability

Since these are sequential events, we multiply the probabilities. So the probability of selecting a Republican and then an Independent is $\frac{7}{18}\times\frac{4}{17}=\frac{28}{306}=\frac{14}{153}$.

Answer:

$\frac{14}{153}$