A city council consists of eight Democrats and seven Republicans. If a committee of four people is selected, find the probability of selecting two Democrats and two Republicans.
Answer
The probability of selecting two Democrats and two Republicans from the committee is approximately \(\boxed{0.431}\)
Step 1 ：Calculate the total number of ways to select a committee of 4 people from a group of 15 using the combination formula: \(C(15, 4) = \frac{15!}{4!(15-4)!} = 1365\)
Step 2 ：Calculate the number of ways to select 2 Democrats from a group of 8 using the combination formula: \(C(8, 2) = \frac{8!}{2!(8-2)!} = 28\)
Step 3 ：Calculate the number of ways to select 2 Republicans from a group of 7 using the combination formula: \(C(7, 2) = \frac{7!}{2!(7-2)!} = 21\)
Step 4 ：Multiply the number of ways to select 2 Democrats and 2 Republicans: \(28 \times 21 = 588\)
Step 5 ：Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: \(\text{Probability} = \frac{588}{1365} \approx 0.431\)
Step 6 ：The probability of selecting two Democrats and two Republicans from the committee is approximately \(\boxed{0.431}\)
