Question

consider a political discussion group consisting of 7 democrats, 6 republicans, and 5 independents. suppose that two group members are randomly selected, in succession, to attend a political convention. find the probability of selecting an independent and then a democrat

(type an integer or a simplified fraction )

Explanation:

Step1: Calculate the total number of group members

The total number of group members is \(7 + 6+5=18\).

Step2: Calculate the probability of selecting an Independent first

The probability of selecting an Independent first is \(\frac{5}{18}\).

Step3: Calculate the probability of selecting a Democrat second

After one Independent is selected, there are \(18 - 1=17\) members left. The probability of selecting a Democrat second is \(\frac{7}{17}\).

Step4: Calculate the combined probability

Since these are two - step dependent events, we use the multiplication rule for dependent events \(P(A\cap B)=P(A)\times P(B|A)\). Here \(A\) is "selecting an Independent" and \(B\) is "selecting a Democrat". So the probability is \(\frac{5}{18}\times\frac{7}{17}=\frac{35}{306}\).

Answer:

\(\frac{35}{306}\)