Birthday Simulation

[Juan González]

So i'm trying to answer the questions "Minimum number of people needed to have more than a 50% chance for a pair to have the same birthday" and "Empirical probability of there being a pair of people with the same birthday in a group of 100 people." My program works fine when answering the first question, but not for the second one. I keep getting 1.01, but I know that's not correct. Does anyone know why simTwo is always 1.01? When I run the debugger in vs code and change the value of T myself, it works fine. Since it's 1.01 I think it's saying that there is a match every single time, but I know that's not true.

import java.util.Arrays;

public class BirthdaySimulation {

    // used to get a random birthday
    public static int selectBirthday(){

        Person per = new Person ();
        int bDay = per.getBirthday();

        return bDay;
    }

    // finds duplicate birthdays in a sorted array
    public static boolean match(int [] arr){

        int len = arr.length;
        int [] temp = new int [arr.length];
        int j = 0, sumArr = 0, sumTemp = 0;

        // Gets rid of the duplicate values
        for (int i = 0; i < len - 1; i++){
            
            if (arr[i] != arr[i + 1]){

                temp[j++] = arr[i];

            }

        }

        // gets the last value in the original array
        temp[j++] = arr [len - 1];
      
        // sums the values in the orginal array
        for (int k = 0; k < arr.length; k++)
            sumArr += arr[k];
        
        // sums the values in the temp array
        for (int l = 0; l < temp.length; l++)
            sumTemp += temp[l];

        // compares the sums of the two arrays. There will be a duplicate if the sums don't match
        if(sumArr != sumTemp){

            return true;

        } else {

            return false;

        }
        
    }

    public static double simulation(int n, double t){

        int i;
        boolean matchFound;  
        int[] birthdays; 

        // stores the number of birthdays 
        birthdays = new int[n];

            // runs the simulation 100 times
            for(i = 0; i <= 100; i++){

            // adds birthdays to the array based on the number of people specified 
            for (int j = 0; j <= n - 1; j++)
            birthdays[j] = selectBirthday();

            // sorts the birthdays from 0 - 365/366
            Arrays.sort(birthdays);

            // checks if there are any duplicate birthdays 
            matchFound = match(birthdays);

            if(matchFound == true)
            t++;

        }

        return t;

    }

    public static void main(String[] args) {

        int n = 1;
        double p = 0.0, t;
        double simTwo;



        // minimum number of people needed to have more than a 50% chance for a pair of people to have the same birthday.
        while (p <= 0.5){
                
            // adds a person each time the simulation is run
            n++;

            t = 0.0;

            p = simulation(n, t)/100;
                
        }

        // empirical probability of there being a pair of people with the same birthday in a group of 100 people.
        simTwo = simulation(100, 0.0)/100;
    
     
        System.out.println("\nMinimum number of people needed to have more than a 50% chance for a pair to have the same birthday: " + n);
        System.out.println("\nEmpirical probability of there being a pair of people with the same birthday in a group of 100 people: " + simTwo + "\n");

    }

}

[Carey Brown]

Still looking ... but your match calc is tortured.

    public static boolean match(int [] arr){
        for (int i = 0; i < len - 1; i++){
            if (arr[i] == arr[i + 1]){
                return true;
            }
        }
        return false;
    }

[Carey Brown]

Juan González wrote:I keep getting 1.01, but I know that's not correct.

Why is it not correct? What do you think it should be?

[Juan González]

Wouldn't 1.01 mean that there is over a 100% chance of there being a match? I may just be interpreting the problem wrong.

[Carey Brown]

You can't use the same simulation method to answer both questions. This is the main() I came up with and the second question is performed without a while() loop.

	public static void main( String[] args )
	{
		double		p = 0;
		int			n = 0;
		while( p <= 0.5 )
		{
			n++;
			p = simulation( n ) / (double)ITERATIONS;
		}
		System.out.println( "n: " + n + "  p: " + p );
		
		n = 0;
		p = 0;
		while( p < 1.0 )
		{
			n++;
			p = simulation( n ) / (double)ITERATIONS;
		}
		System.out.println( "n: " + n + "  p: " + p );
		
		n = 100;
		p = simulation( n ) / (double)ITERATIONS;
		System.out.println( "n: " + n + "  p: " + p );
	}

Output:
n: 23  p: 0.59
n: 56  p: 1.0
n: 100  p: 1.0

[Juan González]

I'm sorry, I don't really understand what you mean.

[Carey Brown]

Perhaps it is floating point rounding error with t++. I used an int for 't'.

[Juan González]

I'll keep trying to figure this out, I appreciate you taking a look

[Carey Brown]

Try changing 't' to be an int and then only at the final stage divide it by 100.0.

[Juan González]

After changing T to an int

If I divide by 100 at the end I get 1.0, but if I divide by 100.0 I still get 1.01.

[Carey Brown]

Change simulation() to take an int for 't' and then define the method as returning an int. Then divide like this
simTwo = simulation(100, 0)/100.0;

[Carey Brown]

I'm pretty sure you're dealing with floating point rounding error.

[Carey Brown]

HERE IT IS
for(i = 0; i <= 100; i++){
this loops for 101 iterations.

[Juan González]

that works, it now says 1.0! Does the probability of there being a pair of people with the same birthday in a group of 100 people being 100% (1.0) make sense?

[Carey Brown]

Now you've got it.

[Juan González]

thank you so much for your help!

[Carey Brown]

Glad to help.

FYI

loop are generally written like this
          for(i = 0; i < 100; i++){
using the '<' operator

[Piet Souris]

Juan González wrote:that works, it now says 1.0! Does the probability of there being a pair of people with the same birthday in a group of 100 people being 100% (1.0) make sense?

You simulate much, by the look of it. Have you tried to come up with a formula for the chance of no same anniverseries in a group of N people?

[Paul Clapham]

Juan González wrote:that works, it now says 1.0! Does the probability of there being a pair of people with the same birthday in a group of 100 people being 100% (1.0) make sense?

It's pretty darn close to 100%, yes.

Have a look at the Wikipedia article Birthday problem; go to the section headed "Approximations" and at the far right you'll see two graphs which answer that question.

[fred rosenberger]

or look at the table where it says:

100 99.99997%