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.

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 \(\boxed{0.431}\)