1. Table of Contents
1. Table of Contents—————————————————————————————————- 2
2. Abstract—————————————————————————————————————- 3
3. Introduction———————————————————————————————————– 3
4. Procedure and results——————————————————————————————— 4
5. Discussion of results———————————————————————————————– 6
6. Conclusion ———————————————————————————————————– 7
7. References ———————————————————————————————————- 7
8. Appendix————————————————————————————————————– 8
2. Abstract
This experiment includes a pair of dice being rolled and then writing the sum of numbers showing dice per roll. The goal of this experiment is to find out what sum is most likely to happen. We should mention that it is all based upon probability, and the data we will get is not reliable or accurate. However, each die has six sides, each with values ranging from one to six. We will do a hundred trials and record the results. After the data of 100 dice rolls are recorded, it will be used to conclude which sum repeats the most. According to the data acquired from the conducted experiment, the sum of seven had a 19% chance of being rolled, which was the highest probability compared to any other sum.
3. Introduction
As this lab is based on probability, I will introduce some basics about it. Probability is a mathematical explanation of how likely an event is going to happen. There are six outcomes when a single die is rolled: 1, 2, 3, 4, 5, 6. The possibility of an event to occur is the number of ways the event can occur versus the total number of outcomes. And in this case, it is 1/6. However, in our experiment, we use two dice, and they both have six sides, so there are thirty-six different combinations of numbers. But there only eleven repeatable sums that could occur; it will go from2-12. According to statistics, the plot of chance for each event is a parabola. According to this analysis, I can hypothesize that rolling two dice a hundred times; seven will be the sum that is most likely to happen, and we will get a bell curve or parabola graph.
4. Procedure and result
I used Excel and two brown dice to complete the experiment. I took both dice in hand and rolled them at the same time. The sum of the dice numbers was recorded in an Excel table into two separate rows. This was repeated 100 times. In the third row, Excel computes the sum of each shot. From the table, I plot the histogram, the frequency of sums versus the sum numbers. Graph 1. shows a histogram, the number of times each sum was obtained from out 100 trial experiments. The histogram reveals a relation between the possible combinations of rolls for a given total and its frequency.
5. Discussion of results
After processing our experiment, I can say that our hypothesis was partially correct. I hypothesized that after rolling two dice 100 times, a sum of 7 would be the most likely to happen, see Graph 1. The other part of the theory was that the sums’ diagram would be a bell or parabola graph, which was not satisfied in full. Some part of Graph 2. looks like a bell graph, but other not. The graph has small outliers with the sum of 10 and 11, but this can be attributed to the lack of trials. For the possibility, it is necessary to have more action. If I made 100 more trials, the results would look even more like the bell curve we were trying to achieve. With more shots, it will bring more uniformity and reduce random chance within our experiment. Figure 3 is a piechart illustrating the results of the experiment. As shown in Figure 3, the number 7 is the most frequent sum rolled, even 19%.
Another parallel analysis, “Investigation of Probability Using Dice Rolling Simulation,” has very different approaches to demonstrate the same findings. In this analysis, a dice roll was performed with three dice. They needed more trials to get a more accurate and uniform result; the report also had a higher rolling dice than I did. Their experiment used a simulation that automatically records the value from three dice rolls, which helps them determine a sum that has a higher frequency. Both experiments produce the same result: a certain number is more frequent because there are more probabilities for the total.
6. Conclusion
The conclusion is that many factors can affect rolling the dice and the probability of getting a specific total. There is more chance to get the number 7 than the rest sums because most dice numbers give a sum of 7. I also exclude other factors like the floor’s roughness, the impulse of dropping the dice differs each time, etc. With all improvements, it was very close to a parabola graph with some outliers, which are not errors but part of an experiment that includes chance. Doing 100 or more trials reduce chance, and it makes an experiment more reliable. However, the result I got is not accurate, and it can vary from case to case as with any other probability experiments.
7. References
➢ Probability Concepts in Engineering(Emphasis on Applications to Civil and Environmental Engineering), by Alfredo H-S. Ang and Wilson H. Tang; Wiley.
➢ Andrew Freda. “Roll the dice — an Introduction to Probability.” Mathematics Teaching in middle school 4.2 (1998): 85–89. Print.
➢ Singh, A. K., Dalpatadu, R. J., & Lucas, A. F. (2011). The Probability Distribution of the Sum of Several Dice: Slot Applications. UNLV Gaming Research & ReviewJournal, 15(2), 109–118.7
8. Appendix
