Simulation of a pair of dice

A die has numbers ranging from 1 to 6. Two dice when rolled together give almost 36 chances. Simulation is used to study random phenomena by replicating the real world with sufficient certainty. To do this, let’s start by listing the possibilities using a pair of dice. There are 36 possible combinations that give a sum between 2 and 12 on both sides. For example, the probability of getting a 2 is very low, which is only 1/36. Similarly, the probability of getting 3 is (1,2) (2,1) which is 2/36 or 1/18. The probability that we obtain a sum of 4 is (1.3) (2.2) (3.1) or the probability of obtaining a sum of 4 with two rolled dice is 4/36 or 1/9.

(2,1,0.027777778,0.027777778), (3,2,0.055555556,0.083333333), (4, 3, 0.083333333, 0.166666667), (5.4 0.111111111, 0.277777778), (6, 5 0.138888889, 0.416666667), (7 , 6 0.166666667,0.583333333), (8.5 0.138888889, 0.722222222), (9.4 0.111111111, 0.833333333), (10, 3.0.083333333, 0.916666667), (11, 2, 0.055555556,0.972222222), (12, 1, 0.027777778, 1)

Above is the number of occurrences of a combination on two dice. The sum of the two numbers varies between 2 and 12, along with it the number of possible combinations of sums that can occur, the next one shown is the probability and the cumulative probability.

Now you can go ahead and generate a lot of random numbers between 0 and 1. These would also be uniform random variations. Based on the random number that appears, the corresponding rank is determined and the sum assigned to that rank is determined. For example, if one generates a random number 0.67, then it occurs between the cumulative probability ranges 0.5833 and 0.722. The corresponding sum assigned to this cumulative probability range is 7. Also, thousands of random numbers must be generated and iterated many times to obtain a perfectly normally generated set of random numbers. This is also verified by the central limit theory.

When this entire model was simulated from two dice rolled in 1000 randomized trials and 1 iteration, the result did not converge with the expected probability of occurrence. The simulated result shows that Three has occurred only once, Seven has occurred five times, Five has occurred 4 times, Four has occurred 3 times, which is different from the number of occurrences and the expected probability of occurrence. This is due to the fact that a faulty RndNum generator may have been used and also the fact that the dice pair system has not been simulated for a sufficient number of trials and replicates. Since a thousand random numbers cannot be pasted in this tutorial, it has been omitted. Doing so will help the RndNumbers converge to a normal distribution and will also help calculate the occurrences of the totals in the simulated system.