Question

Language: JAVA(Netbean)

Using a hash set to do a Monte Carlo analysis of the birthday paradox. The paradox states that the odds of 2 people in a group sharing a birthday is surprisingly high.

A Monte Carlo analysis is using random numbers to simulate actual probable outcomes.

Test your code for various numbers of people.

Here is pseudo code of the algorithm:

Set number of collisions to zero

Loop (10 to100 by 10)

   Loop:

      Generate a birthday. (use 1-365)

      See if it is already in the set. If it is count as a collision and end the loop.

      Add to the set.

Print out the number of collisions as a probability P.

For example, if you ran 50 people and got 25 collisions P = 0.5

The probability of 100 is around 1.0. P can never exceed 1.0. If you exceed 1.0 you are counting collisions in a group more than once.

Example Output:

--------------------Configuration: <Default>--------------------

After 100000 tests there were 11446 occurrences of shared birthdays in a set of 10 people.

Probability: 0.11446

After 100000 tests there were 41031 occurrences of shared birthdays in a set of 20 people.

Probability: 0.41031

After 100000 tests there were 70455 occurrences of shared birthdays in a set of 30 people.

Probability: 0.70455

After 100000 tests there were 89061 occurrences of shared birthdays in a set of 40 people.

Probability: 0.89061

After 100000 tests there were 97043 occurrences of shared birthdays in a set of 50 people.

Probability: 0.97043

After 100000 tests there were 99454 occurrences of shared birthdays in a set of 60 people.

Probability: 0.99454

After 100000 tests there were 99926 occurrences of shared birthdays in a set of 70 people.

Probability: 0.99926

After 100000 tests there were 99986 occurrences of shared birthdays in a set of 80 people.

Probability: 0.99986

After 100000 tests there were 99999 occurrences of shared birthdays in a set of 90 people.

Probability: 0.99999

After 100000 tests there were 100000 occurrences of shared birthdays in a set of 100 people.

Probability: 1.0

Process completed.

Answer 1

PLEASE GIVE IT A THUMBS UP, I SERIOSUL NEED ONE

import java.util.HashSet;
import java.util.Random;

class MonteCarloBirthdayParadox {

public static void main(String[] args){
Random r = new Random();
int day;
int count = 0;
for(int i = 10; i <= 100; i += 10){
count = 0;
for(int j = 0; j < 100000; ++j){
HashSet<Integer> set = new HashSet<>();
for(int k = 0; k < i; ++k) {
day = 1 + r.nextInt(365);
if (set.contains(day)) {
++count;
break;
} else {
set.add(day);
}
}
}
System.out.printf("After 100000 tests there were %d occurrences of shared birthdays in a set of %d people\n", count, i);
System.out.println("Probability: " + count / 100000.0);
}
}

}