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#include <iostream> #include <cmath> #include <iomanip> #include <vector> using namespace std; // Function to calculate binomial coefficient int binomialCoefficient(int n, int k) { if (k > n) return 0; if (k == 0 || k == n) return 1; int res = 1; for (int i = 0; i < k; ++i) { res *= (n - i); res /= (i + 1); } return res; } // Function to calculate binomial probability double binomialProbability(int n, int k, double p) { return binomialCoefficient(n, k) * pow(p, k) * pow(1 - p, n - k); } int main() { const int n = 3; // number of trials (coins) const double p = 0.3; // probability of heads const int totalTosses = 100; // total number of trials vector<double> probabilities(4); vector<double> expectedFrequencies(4); // Calculate binomial probabilities and expected frequencies for (int k = 0; k <= n; ++k) { probabilities[k] = binomialProbability(n, k, p); expectedFrequencies[k] = probabilities[k] * totalTosses; } // Print the results cout << fixed << setprecision(2); cout << "Number of Heads\tProbability\tExpected Frequency\n"; for (int k = 0; k <= n; ++k) { cout << k << "\t\t" << probabilities[k] << "\t\t" << expectedFrequencies[k] << "\n"; } return 0; }
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