Day-4_BinomialDistribution-I.cpp

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

/*
        p = b/b+g;
        q = 1 - p;
        prob = sum(i=3 to i=6)(p^i)(q^(6-i));
*/

double b = 1.09, g = 1;  // given

int fact(int n)
{
    if(n<2) return 1;
    return n*fact(n-1);
}

double nCr(int n, int r)
{
    return fact(n)/(fact(r)*fact(n-r));
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */ 
    
    double p = b/(b+g);
    double q = 1 - p;
    
    double prob = 0.0;
    
    for(auto i=6; i>=3; i--)
    {
        prob += nCr(6, i)*pow(p, i)*pow(q, 6-i);
    }
    printf("%0.3f\n", prob);
    
    return 0;
}