Microsoft Visual C# Example: The Binomial Probability

	Microsoft Visual C# Example: The Binomial Probability

Introduction

The binomial probability is a measure of the likelihood (probability) of successfully getting a certain of occurrences out of a total number of trials. For example, imagine you have planted peas that produced various offsprings. Also imagine that, from previous tests, you have come to realise that the probability of getting green peas out of your farm is 0.75. Now imagine you plant some peas and they produce five offsprings. You may want to find out the probability of getting three peas.

The formula to calculate the binomial probability is:

The factors in this formula are:

Factor	Description
n	The number of trials
x	The number of successful trials among n values. The values of x go from 0, 1, 2, ..., to n
p	The probability of success in a (any one) trial
q	The probability of failure in a (any one) trial. q is considered as q = 1 - p

Application: Creating an Application

Start Microsoft Visual Studio
To create a new application, on the main menu, click File -> New Project...
In the middle list, click Windows Forms Application
Change the Name to BinomialProbability1
Click OK
In the Solution Explorer, right-click Form1.cs and click Rename
Type Exercise.cs and press Enter

Design the form as follows:

Control	(Name)	Text	TextAlign	Other Properties
Label		&Number of Trials:
TextBox	txtTrials		Right
Label		Number of &Successes:
TextBox	txtSuccesses		Right
Label		&Probability of Success:
TextBox	txtProbabilitySuccess		Right
Button	btnCalculate	C&alculate
PictureBox				BackColor: Black Size -> Height: 2
Label		&Binomial Probability:
TextBox	txtBinomialProbability		Right
Button	btnClose	Close

Double-click the Calculate button on the form

Change the file as follows:

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace BinomialProbability1
{
    public partial class Exercise : Form
    {
        public Exercise()
        {
            InitializeComponent();
        }

        private static long Factorial(long x)
        {
            if (x <= 1)
                return 1;
            else
                return x * Factorial(x - 1);
        }

        private static long Combination(long a, long b)
        {
            if (a <= 1)
                return 1;

            return Factorial(a) / (Factorial(b) * Factorial(a - b));
        }

        private double BinomialProbability(int trials, int successes,
        				   double probabilityOfSuccess)
        {
            double probOfFailures = 1 - probabilityOfSuccess;

            double c = Combination(trials, successes);
            double px = Math.Pow(probabilityOfSuccess, successes);
            double qnx = Math.Pow(probOfFailures, trials - successes);

            return c * px * qnx;
        }

        private void btnCalculate_Click(object sender, EventArgs e)
        {
            int nbrOfTrials = 0, nbrOfSuccesses = 0;
            double probOfSuccesses = 0.00;
            double binomial = 0.00;

            try
            {
                nbrOfTrials = int.Parse(txtTrials.Text);
            }
            catch (FormatException)
            {
                MessageBox.Show("The number of trials is not valid",
                                "Binomial Probability");
            }

            try
            {
                nbrOfSuccesses  = int.Parse(txtSuccesses.Text);
            }
            catch (FormatException)
            {
                MessageBox.Show("The number of successes is not valid",
                                "Binomial Probability");
            }

            try
            {
                probOfSuccesses = double.Parse(txtProbabilitySuccess.Text);

                binomial = BinomialProbability(nbrOfTrials,
                 			       nbrOfSuccesses,
                 			       probOfSuccesses);
                txtBinomialProbability.Text = binomial.ToString();
            }
            catch (FormatException)
            {
                MessageBox.Show("The number of trials is not valid",
                                "Binomial Probability");
            }
        }
    }
}

Return to the form and double-click the Close button

Implement the event as follows:

private void btnClose_Click(object sender, EventArgs e)
{
    Close();
}

Return to the form
To execute, press F5
Enter some values and click Calculate
Close the form and return to your programming environment


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