N个事件中最少发生K个事件的概率c++实现

在概率论中，计算N个独立事件中有至少发生K个事件的概率通常涉及二项分布，特别是当每个事件发生的概率相同时。二项式系数（也称为组合数）可以用来表示从N个事件中选择K个的方式数量，而这个概率可以通过公式 P(X >= K) = C(N, K) * p^K * (1-p)^(N-K) 计算，其中p是单个事件发生的概率，(1-p)是不发生的概率。

以下是C++的一个简单实现：

#include <iostream>
#include <cmath>

// Calculate binomial coefficient (n choose k)
int binomialCoefficient(int n, int k) {
    if (k > n || k < 0 || n < 0) return 0;
    int result = 1;
    for (int i = 0; i < k; ++i) {
        result *= (n - i);
        result /= (i + 1);
    }
    return result;
}

// Calculate the probability of at least K successes in N trials with probability p
double calculateMinimumProbability(int N, int K, double p) {
    // Probability of exactly k or more events happening is complement of less than k events
    double probability = 1.0;
    for (int i = K; i <= N; ++i) {
        probability -= static_cast<double>(binomialCoefficient(N, i)) * pow(p, i) * pow(1 - p, N - i);
    }
    probability = std::max(probability, 0.0); // Ensure probability doesn't go below zero due to rounding errors
    return probability;
}

int main() {
    int N = 10; // Number of events
    int K = 5; // At least K events should happen
    double p = 0.5; // Probability of each event

    double minProbability = calculateMinimumProbability(N, K, p);
    std::cout << "The probability that at least " << K << " out of " << N << " events occur is: " << minProbability << "\n";
    
    return 0;
}

在这个例子中，`calculateMinimumProbability`函数接受三个参数，N、K和p，然后计算并返回至少发生K个事件的概率。