Point(S) possible
Consider a pollitical discussion group consisting of 9 Democrets, 9 Republicans, and 3
Independents. Suppose that two group members are randomly selected, in succession, to
attend a polliteal convention. Find the probabilly of selecting two Denocrats.
(Type an integer or a simplified fraction.)

Question

Point(S) possible
Consider a pollitical discussion group consisting of 9 Democrets, 9 Republicans, and 3
Independents. Suppose that two group members are randomly selected, in succession, to
attend a polliteal convention. Find the probabilly of selecting two Denocrats.

(Type an integer or a simplified fraction.)

UpStudy AI · Accepted Answer

Let the total number of group members be  
$$
9 + 9 + 3 = 21.
$$

**Step 1:**  
The probability that the first selected member is a Democrat is  
$$
\frac{9}{21}.
$$

**Step 2:**  
Once a Democrat is selected, there remain 8 Democrats out of a total of 20 members. So, the probability that the second selected member is also a Democrat is  
$$
\frac{8}{20}.
$$

**Step 3:**  
The overall probability of selecting two Democrats in succession is the product of the two probabilities:
$$
\frac{9}{21} \times \frac{8}{20} = \frac{72}{420}.
$$

**Step 4:**  
Simplify the fraction by dividing the numerator and denominator by the greatest common divisor, which is 12:
$$
\frac{72 \div 12}{420 \div 12} = \frac{6}{35}.
$$

Thus, the probability of selecting two Democrats is  
$$
\frac{6}{35}.
$$
The probability of selecting two Democrats is $$\frac{6}{35}$$.

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