Respuesta :
Answer:
The probability of selecting two Democrats and two Republicans is 0.4242.
Step-by-step explanation:
The information provided is as follows:
- A city council consists of seven Democrats and five Republicans.
- A committee of four people is selected.
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!\times (n-k)!}[/tex]
Compute the number of ways to select four people as follows:
[tex]{12\choose 4}=\frac{12!}{4!\times (12-4)!}=495[/tex]
Compute the number of ways to selected two Democrats as follows:
[tex]{7\choose 2}=\frac{7!}{2!\times (7-2)!}=21[/tex]
Compute the number of ways to selected two Republicans as follows:
[tex]{5\choose 2}=\frac{5!}{2!\times (5-2)!}=10[/tex]
Then the probability of selecting two Democrats and two Republicans as follows:
[tex]P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242[/tex]
Thus, the probability of selecting two Democrats and two Republicans is 0.4242.
