Dice Probability:
The Outcome of Dice Being rolled 100 Times
Abstract:
A dice has six sides to it that ranges from one to six. The purpose of this experiment is to roll a two fair six sided dice one hundred times, in order to find out the outcome of the numbers 2-12 occurring out of 100 times. The two pairs of dice will be rolled repeatedly 100 times and the data will be recorded throughout the experiment. According to the results of the experiment and as shown in the bar graph and pie chart, the number that was displayed the most was seven. Seven had a 16% chance of being rolled, representing the highest probability.
Name: Russell Mohammed
Date: 3/19/19
Introduction:
The dice probability experiment consist of rolling a two fair six sided dice 100 times. Probability is the extent of which an event is likely to occur, measured by the ratio of the case occurring over the number of cases possible. By rolling the pair of dice, there is an equal probability that the dice will land on any given side, creating a sum from 2-12. The main purpose of this experiment is to figure out which sum of number can occur the most and represent the highest probability. I predict that the number seven will have the best odds of being the highest sum from the two six sided dice.
Materials:
- Two six sided dice
- A pencil to write down the results
- A paper to record the results
Procedure:
- First, gather the materials together, the two six sided dice, the pencil and the paper.
- Then, begin to roll the dice for the first time out of 100 times.
- Next, record the data of what was rolled from the dice.
- After, repeat steps one to three, 100 times.
- Finally, after the data is recorded create a bar graph and pie chart to represent the sum of the numbers that occured.
Results:
Figure 1
Figure 1 displays a bar graph representing the probability of each number from 2-12 appearing out of 100 times.
Figure 2
Figure 2 displays a pie graph representing the percent of each number from 2-12 occurring out of 100 times.
Analysis:
After conducting my experiment of rolling the pair of dice 100 times, the number that occured the most from 2-12 was seven. The number seven occurred 16 times with the number 10 and 12 being very close behind with an outcome of 14. With the number seven being the number to occur the most, my hypothesis was correct. The chance of seven having the highest outcome was due to the idea of seven being a lucky number. Both the bar graph and pie chart represent the data of how many times the sum of numbers between 2-12 can appear aftering rolling the dice for a 100 trials. My results, can also be compared to the study, “The probability distribution of the sum of several dice: Slot Applications.” In this study, the researchers Ashok K. Singh, Rohan J. Dalpatadu and Anthony F. Lucas used the method of moment generating function(mgf) to derive the probability of the sum of (K) dices. The (K) stands for the sum of how many dices are being rolled. Throughout, their experiment of using the sum of two fair sided dice, the number seven was derived the most out of 36 trials. However, what made our research different was that Ashok K. Singh, Rohan J. Dalpatadu and Anthony F. Lucas developed a function in solving the probability of which sum of number will occur the most whereas, my outcome was developed through rolling the dice 100 times.
Conclusion:
In conclusion, after conducting the dice probability experiment, my hypothesis of the number seven having the highest outcome was correct. The idea of rolling the two sided fair dice, gave the sum of numbers an equal chance of occuring. If both dice were not fair, the experiment would not create an equal probability for the sum of numbers. The results of the numbers 2-12 being derived can be referred to in figure one that represents a bar graph or in figure two that portrays a pie chart. With the study of my results and the results that came from the experiment done by Ashok K. Singh, Rohan J. Dalpatadu and Anthony F. Lucas, “The probability distribution of the sum of several dice: Slot Applications,” the number seven represents a high chance to occur when rolling two pairs of fair sided dice.
Work Cited:
Singh, A.K., Dalpatadu, R.J., & Lucas, A.F. 1 Oct. 2011.The Probability Distribution of the Sum of Several Dice:Slot Application. Retrieved from https://web-b-ebscohost-com.ccny-proxy1.libr.ccny.cuny.edu/ehost/detail/detail?vid=3&sid=3bcea5e3-a064-4ed5-a6a4-789dbb80007d%40pdc-v-sessmgr06&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#AN=69735833&db=a9h
Appendix
Rolling Number Number of Rolls
| 2 | 2 |
| 3 | 4 |
| 4 | 3 |
| 5 | 5 |
| 6 | 10 |
| 7 | 16 |
| 8 | 12 |
| 9 | 12 |
| 10 | 16 |
| 11 | 6 |
| 12 | 14 |
