Question

Write a program that determines the probability of tossing a coin 10 times and getting exactly 0, 1, 2, 3, etc. heads. This is the binomial probability distribution. Store the probability in an array. You could get 0 heads or 10 heads or anything inbetween.

Use a for loop. The for loop will go from 0 to 10 inclusive. Use r as the number of successes. So r will go from 0 to 10. The probability of a success is .5, and also the probability of a failure is .5.

Print out in table form, column 1=r; goes 0 to 10, and then column 2; the probability of r.

Use 4 decimal places for the probability. You know if you get the correct answers because The sum of all the probabilities is 1.0, and all probabilities are in the range of 0 to 1 inclusive.

In C++, prefer visual studios but not required.

Answer 1

The code is as follows:

#include <iostream>
#include<cmath>
#include <sstream>
#include <iomanip>

using namespace std;

// Returns factorial of n
int fact (int n)
{
int s = 1;
for (int i = 2; i <= n; i++)
    s = s * i;
return s;
}

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

int main ()
{
double prob[11][2];       //array to store the probability values
double p = 0.5;       //probability of pass
double f = 0.5;       //probability of failure
double x = 0;
int n = 10;           //number of tries

for (int i = 0; i <= 10; i++)
    {
      x = nCr (n, i) * pow (p, i) * pow (f, n - i); // The formula is used to calculate the probability
      //following three lines of code is used for rounding the value to 4 decimal places
      stringstream tmp;
      tmp << setprecision(4) << fixed << x;
      double new_val = stod(tmp.str());
      prob[i][0] = i;
      prob[i][1] = new_val;
    }

cout << "The probability of tossing a coin 10 times and getting exactly 0, 1, 2, ... ,10 heads is as follows: "    << endl;

for (int j = 0; j <= 10; j++)
    {
        cout << "X = " << prob[j][0] << "   P = " << prob[j][1] << endl;
    }

return 0;
}