------
## 最终结论
```python
import math

def binomial_probability(n, k, p):
    # 计算组合数 C(n, k)
    combination = math.factorial(n) / (math.factorial(k) * math.factorial(n - k))
    # 计算二项式概率
    probability = combination * (p ** k) * ((1 - p) ** (n - k))
    return probability

# Test cases
assert binomial_probability(10, 5, 1.0/3) == 0.13656454808718185
assert binomial_probability(11, 6, 2.0/4) == 0.2255859375
assert binomial_probability(12, 7, 3.0/5) == 0.227030335488
```