Question

consider a political discussion group consisting of 5 democrats, 6 republicans, and 3 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 an independent.

(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of members

Total members = \(5 + 6+3=14\)

Step2: Probability of selecting a Democrat first

Number of Democrats is \(5\). Probability \(P(D)=\frac{5}{14}\)

Step3: Probability of selecting an Independent second

After selecting a Democrat, number of remaining members is \(13\). Number of Independents is \(3\). Probability \(P(I)=\frac{3}{13}\)

Step4: Use multiplication rule for dependent events

\(P(D\text{ and }I)=P(D)\times P(I)=\frac{5}{14}\times\frac{3}{13}\)

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Answer:

\(\frac{15}{182}\)