Radhyyah Hossain

10/23/19

 

Two Dice, One Winner: A Lab Report on Dice Probability

 

Abstract:

          This experiment is about using two dice to find dice probability. The purpose of this experiment is to roll a pair of dice a hundred times and to see which number, the sum of the two dice, shows up the most. The dice are six-sided dice which means there can be 36 possible outcomes with a ⅙ probability. The experiment focused mainly on the outcome probability of the dice which the highest probability was found to be the sum of 7 while the lowest was found to be the sum of 12. This probability can be caused by different factors such as weight and smooth or rough areas. 

 

Introduction:

          In the case of probability, it is always best to have a large number of trials. But what is probability exactly and why do we need a large number of trials? Probability is the chance that something might happen and so having a large number of tests, gives a clearer explanation of what might happen. 

          In this experiment, two dice were rolled a hundred times to see what number has the highest probability rate by taking the sum of the two dice. Since there are two dice which are both six-sided, there would be 11 possible outcomes because the sum of 2 dice can’t equal to one. If there are two dice, the sum that would have the least number of outcomes would be 12. 

 

Materials:

1. Two dice.
2. Pen.
3. Paper.

 

Method (Steps):

1. The two dice were rolled a hundred times.
2. Each time the two dice were rolled, the sum of the two numbers shown on the dice was added. 
3. The sums were recorded after every roll. 
4. The sums were recorded on a paper and the total for each combination for each sum was recorded. (ex: combinations equaling 6 (1/5, 2/4, 3/3) were each separated by how many times it appeared.)
5. There were two separate charts; one chart was for the sums and how many times they appeared and the other chart was for the number of each combination for each sum (Shown in appendix).
6. The percentage for how probable each sum was calculated. 

 

Results: 

          After gathering data and converting it into a bar graph, the graph shows that the sum of seven has the greatest probability in percentage. It also shows that the percentages for the sums from 1-6 are similar to the percentages for the sums from 8-12. 

Figure 1: The bar graph shows the sum which had the greatest probability in percentage is 7.  

 

Analysis:

          Figure 1 shows that seven has the highest probability rate of 21% while the other sums are lower. The two numbers that come close to the highest rate are sums six and eight. Six has a 15% probability rate while eight has a 17% probability rate. The hypothesis was that since there are two dice, the sum that would have the least number of outcomes would be 12. The experiment and the chart show that 12 has the least probability rate because the only way to get a sum of 12 is 6+6 and getting two of the same numbers at the same roll is hard to get. This experiment does prove the hypothesis because the probability in the percentage of getting a sum of 12 is 2%. However; how do we know that rolling dice is truly random, thus, giving a more accurate result? 

          There are many things that can affect the randomness of dice such as friction, and the initial position of the dice. Jan Nagler and Peter H. Richter from the Institute for Theoretical Physics at the University of Bremen, Germany; published a research paper about the randomness of dice on the New Journal of Physics. They studied the general symmetry of dice of unequal masses, loaded and unloaded dice. Loaded dice are dice that are a little bit heavier on one side than others to get the desired number. The research paper concludes that dice that are heavier tend to bounce more before coming to a rest at an angle and that lighter or unloaded dice bounce less because of how light it is and the effect of friction. In the article it states:

          It seems intuitively clear that the heavier mass dominates the relaxation process: the reflection has a bigger effect on the lighter mass than vice versa. Therefore, one expects the larger mass to come to rest earlier than the smaller and, hence, to exhibit more bounces before the final state is determined. (Jan Nagler, Peter H. Richter 10)

          The heavier the dice is, the more it bounces because of the amount of energy that is stored in the dice when dropped at a certain height. Using this research, it can be inferred that if a lighter dice was dropped at a certain height and angle, then it would bounce less because of more friction. Assuming that the two dice used for this experiment was a lighter dice and the fact that the two dice were rolled on carpet/ rougher area, it can be inferred that the initial positions of the dice caused the sum of seven to have a higher probability rate. Since the dice were rolled on a rough area, the friction caused the dice to not move faces as much and thus resulting in more sum of six-to-eight outcomes. 

 

Conclusion:

          This experiment showed that the sum of seven has a higher probability rate than any other sums and that there are a lot of factors that come into play when wanting to get a truly random set of data. This experiment also shows that rolling dice is not perfectly random since friction and weight, and height are important factors. The point of this experiment was to show the probability rate of a certain sum of numbers. Practical applications of this experiment can be used when playing board games that have dice. 

 

Work Cited:

• Jan Nagler and Peter H Richter. Published: 2010. New J. Phys. https://iopscience.iop.org/article/10.1088/1367-2630/12/3/033016/pdf

 

Appendix:

• Microsoft excel used to make Figure 1. 
• Data for the total number of each combination for each sum of the experiment:

 

Sums	Combinations/ Number of Appearances
2	1+1 4 Total: 4
3	1+2 6 Total: 6
4	1+3 7 2+2 2 Total: 9
5	1+4 5 2+3 5 Total: 10
6	1+5 7 2+4 5 3+3 3 Total: 15
7	1+6 5 2+5 9 3+4 7 Total: 21
8	2+6 6 3+5 8 4+4 3 Total: 17
9	3+6 8 Total: 8
10	4+6 4 5+5 1 Total: 5
11	5+6 3 Total: 3
12	6+6 2 Total: 2
	Whole Total: 100 rolls.