Question

Question 1:

Write a Java program that computes the exact probability distribution for the sum of two dice. Run experiments to validate this calculation simulating N dice throws, keeping track of the frequencies of occurrence of each value when you compute the sum of two random integers between 1 and 6. How large does N have to be before your empirical results match the exact results to three decimal places?

Answer 1

Hi

Here is the java code to simulate the rolling of two dices and finding the probability of having the sum in the range of 2 to 12 inclusive.

We are doing the experiment 100000 times and printing the probabilities of the actual and expected.

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import java.util.Random;

public class Dice {
    public static void main(String[] args) {

        int sum = 0;
        int dice1 = 0;
        int dice2 = 0;
        int actual = 0;
        int[] occurenceCount = new int[13];

        int[] ways = {0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1};

        for (int i = 0; i < 100000; i++) {
            sum = 0;
            dice1 = new Random().nextInt(6) + 1;
            dice2 = new Random().nextInt(6) + 1;
            sum = dice1 + dice2;
            occurenceCount[sum]++;
        }

        for (int i = 0; i < 13; i++) actual += occurenceCount[i];

        System.out.printf("%-4s %s %-11s %s%n", "Sum", "Total", "Expected",
                "Actual");
        for (int i = 2; i < 13; i++) {
            System.out.printf("%-4d %-5d %-10.4f %2.4f%n", i, occurenceCount[i],
                    100.0 * ways[i] / 36, 100 * (double) occurenceCount[i] / actual);
        }
    }
}

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thank you !