// probability.cpp
//
// Abdul Khan
// 01/30/02
//
// Find the probability that a given even will occur x times in N trials
// Test case returned Prob(100,30)= 2.31707e-05 and Prob(1000,400)= 4.63391e-11

//#include "stdafx.h"
#include <iostream.h>
#include <math.h>

double choose(const double N, const double x)
{
        double c = 0;
        for (int i=1;i<=N;i++)
        {
                c += log(i);
                if (i <= x ) c -= log(i);
                if (i <= N-x) c -= log(i);
        }
        return pow(exp(1),c);
};


int main(int argc, char* argv[])
{
        double N,x;

        double p = 0.5;

        do {
        cout << "This program will calculate the probability that an N evenly chanced\n";
        cout << "events will result in one of the outcomes exactly x times\n";
        cout << "Please enter N ";
        cin >> N;
        cout << "Please enter x ";
        cin >> x;
        cout << "The chances of that are " << (choose(N,x)*pow(p,x)*(pow((1-p),(N-x)))) << endl;
    } while (x && N);
		return 0;
};