Abstract:
Understanding the concept of probability with the use of statistics can be difficult to analyze without a set goal. The purpose of conducting this experiment is to understand how probability relates and works when using 2 dice. Therefore, conducting this experiment in 100 trials will provide better and accurate information about the percentage that it takes to roll any number, in this case I will be focusing on the number 7. After recording all 100 trials, my results ended up contradicting my hypothesis because the number 7 wasn’t the highest number I rolled, it was 8. The percentage of rolling a 7 in 100 trials was 17% while rolling the number 8 was 20%, 1/5 of my rolls were 8. There was only a 3% difference between 8 and 7, indicating that the probability in this experiment is always changing.
Aldo Falcon March 21, 2019
Introduction
Have you ever wondered what’s the probability of rolling that single number you need to win in a game or a challenge? Dices can be used for many things such as in a casino when you are gambling, Board games such as Monopoly or Dungeons and Dragons. The use of a die can be applied to many things. Therefore, testing out the probability of a number, for example the number 7, is very hard to guess when knowing that you have a 16% chance of rolling a 7 or any number but that’s not always the case. When you add another die, making a total of 2 dice, the probability of rolling a number from 1-12 changes and the possibilities are limitless. The purpose of this experiment is getting a better understanding of probability using 2 dice. If the probability of rolling any number in a single die from 1-6 is 16%, then adding a second dice, the sum of rolling a 7 will be greater because now our chances have increased from 16% to 32%.
Materials:
- 2 dice
- 1 pen/pencil
- Plenty of paper to record the data of numbers rolled in 100 trials
Methods:
Step by Step Instructions:
- Find 2 rolling dice to perform this experiment
- Place both dice on your hand and scramble them around your palm
- Throw the dice on the floor or any surface
- Record the number of dots both dice have when facing up onto the paper
- Name it as Trial #1
- Add the number of dots on the first dice and the second dice as the Total of Both Dice rolled
- Repeat steps above until you reach 100 trails
Results
Figure #1
- In Figure #1, the colors represent the sum of both sides in 2 dices while the percentage represent the amount of times that specific number was shown from 100 trials. Note that probability of the numbers 1,2, and 12 was 0% which is why they are all in the same category.
Figure 2
| Numbers of each side in a Die | Total # drawn of each side in Dice 1 | Total # drawn of each side in Dice 2 | % of each side drawn in both Dice |
| 1 | 17 | 18 | 18% |
| 2 | 21 | 22 | 21% |
| 3 | 18 | 14 | 16% |
| 4 | 12 | 18 | 15% |
| 5 | 15 | 13 | 14% |
| 6 | 16 | 15 | 16% |
- In Figure 2, I decided to add up all the amount of times a number appeared for each individual die. I did this for both dice, and we can see that numbers are constant for the most part. Then I calculated the percentage that it would take to roll a specific number on a die as shown on the right side of the chart.
Analysis
First, I know that rolling a one with two dices is impossible but surprisingly, I never rolled a total 2 or 12 which means that the combinations of (1&1) with (6&6) never occurred. In Figure 2, I noticed that the chances of rolling any number was around 16% like I mentioned in my hypothesis. Analyzing this chart, I noticed that the chances of drawing the number 8 by combining the numbers in both dice were higher than the combination of any other number. Number 7 and number 5 was the other 2 greatest numbers drawn. In Figure #1 I can tell that my hypothesis wasn’t fulfilled because out of 100 trials, the percentage of rolling a number eight was 20%. It was only a 3% difference when looking at the number seven which was 17%. The possible outcome of eight being the most number drawn could be because of many different factors. The distance that both dice traveled before stopping was different for each individual trial. The way that I rolled the dice around my hand could be a possible factor as well as the number that appeared facing up on my hand before I rolled them was different in each trial. The height in which the dice feel from my hand to the floor could be another factor as to why the number 7 didn’t come up as much as the number 8. They’re many different factors that can change our results and therefore, the probability in this case is limitless.
To better understand this concept of probability we can look over at the article, “Unders and Overs: Using a Dice Game to Illustrate Basic Probability Concepts” by Sandra Hanson McPherson. In this article she illustrates a game known as “Unders and Overs” to explain the concept of probability. In Sandra’s result we see that the number rolled the most was both six and seven in a shorter amount of trial. This explains that the probability of rolling any number, not just 7, is something that isn’t constant and through a game it’s easier to understand the basics. In my results I didn’t get a sum of 2 or 12 but in Sandra’s chart she managed to roll both numbers. There are probably many factors that depend on the outcome of rolling any dice and which is why results will very within each experiment.
Conclusion
After conducting this experiment 100 times, I can conclude that when dealing with probability, there can be many factors that can affect the results. In the end my hypothesis wasn’t accomplished in 100 trials. The probability of rolling a total of eight was 20% or 1/5, which was only 3% higher than rolling a total of seven. Perhaps if more trials were added then our results could’ve changed, and possibly even rolling a total of 2 or 12.
Work Cited
- McPherson, S. H. (2015). Unders and Overs: Using a Dice Game to Illustrate Basic Probability Concepts. Teaching Statistics, 37(1), 18–22. https://doi-org.ccny proxy1.libr.ccny.cuny.edu/10.1111/test.12033
Appendix
Looking at the chart above, it represents the 100 trials conducted when rolling and recording the results of 2 rolling dice. The charts are split into 4 columns, on the farthest left I have the number of trials conducted, followed by 2 columns each one for each die. After recording the numbers drawn on both dice, I added them up and showed the results on the right side of the chart labeled, Total of Dice 1 & 2. Looking at this graph, one can tell that I never drew the total numbers 2, 12, and 1 was an impossible outcome when dealing with 2 dice. Realizing that there were only 9 possible outcomes out of 12 indicated that the probability of rolling a 2 or a 12 is unknown in my case. In addition, knowing that I only had 9 out of 12 possible outcomes, I can see why I had a greater chance of rolling the rest of the numbers that didn’t include 1,2, and 12. Another interesting point is that the number 8 appeared more than the number 7 by 3%. In addition, if you look along the graph, you notice that double digits weren’t drawn as much compared to single digits. The chances of rolling double digits, in this case it only included the numbers 10 and 11, was only 9% overall. This chart really Illustrates that the possibility of rolling any number is limitless because many factors can come into play such as, the way you rolled the dice, the distance it traveled, etc.
