A Measure of Uncertainty:

The Probability for Rolling a Dice

The goal of this experiment is to evaluate the total number I will most likely get after rolling two dice for a total of 100 times. I would have to roll my two dice and record the sum, which would be between 2-12. After repeating the steps of rolling and recording the sum, I found that nine was the most probable number, where two and twelve were the least probable number. I was able to compile my data and represent it on the table. In order to get a better perspective of which sum was landed on the most and which was landed the least, I also organized a pie chart.

 

Wally Hasnat

3/21/19

 

In this experiment, I find the probability of each likely outcome after rolling two dice. The probability of an event is how often it is expected to occur, so I want to evaluate which sum I roll the most and which one I roll the least. To find the probabilities of these outcomes, I have to be aware of how many total possible outcomes there are and how often each outcome occurs. Since there are six sides on each die, we can figure out that there is a total of 36 possible outcomes when rolling our two dice. Now, when rolling two dice, the result is completely random. One roll has nothing to do with the other so this gives us a better chance of randomizing our outcomes. After rolling the dice 100 times, I believe that 7 will the most probable sum and will be rolled more than any other outcome.

 

Materials

• A pair of dice
• Pen or pencil
• Piece of paper

 

Procedure

1. Roll the pair of dice.
2. Record the sum of two dice on paper.
3. Repeat steps one and two 99 more times.
4. Compile the data found and identify the number of times each number (2-12) was landed.
5. Represent it on a table or graph.

 

After recording the number of times each outcome was rolled, I found that the number nine was rolled the most amount of times with a total of 16 times. Additionally, twelve was found to be the least probable as I was only able to roll it once.

 

Figure 1:

 

This bar graph properly shows the outcomes with the most amount of rolls, the least amount of rolls, and the same amount of rolls.

 

                                     Figure 2:

This pie chart gives us a better perspective of which portions were landed on the most and least as well. As you can see, most of them look around the same size, with the exception of 12 as it was the least probable. It is also prevalent that 9 was the highest rolled sum as it has the biggest portion.

 

After completing my experiment, I found that my hypothesis was incorrect as 9 was the most probable sum instead of 7. I thought that seven would be the most probable number because I supposed that it was the only sum of two dice that can be achieved through a total of six combinations. However, this theory is not always accurate. Additionally, there are many factors into having expectations when rolling two dice as many have preconceived ideas from past experiences.

According to other experiments, seven was the number that was stated to be the most probable as well. I noticed that the most probable outcomes are in the center area where 7,8 and 9 are and the further you go from the middle the less likely it is to be rolled, such as 2 and 12. In fact, these two numbers did come up the least because rolling a one or six on both is considered to be lucky. Although my hypothesis was incorrect, my graph does relate to the simulations found online for other experiments.

I also noticed that the probability of accuracy of expectation depends on the number of trials conducted. This was apparent during my first ten trials where 7 was the only number that was repeated. This relates to an experiment that was done by 6th-gradeProbability of Two Dice students that highlighted expectation and variation. After conducting their experiment of rolling two dice for about 30 times, all students had the same conclusions. They stated how their expectations were not always correct and that variations can always change. Similar to them, after conducting my experiment, I was also able to understand that increasing the number of times rolled would decrease the variations of your outcomes.

 

Works Cited

• Taylor, Courtney. “What Are the Probabilities for Rolling Two Dice?” ThoughtCo, ThoughtCo, 25 Oct. 2018, www.thoughtco.com/probabilities-of-rolling-two-dice-3126559.

 

• Watson, Jane, and Lyn English. “Expectation and Variation with a Virtual Die.” Eric.ed.gov, Australian Association of Math Teachers, 2015, web-a-ebscohost-com.ccny-proxy1.libr.ccny.cuny.edu/ehost/pdfviewer/pdfviewer?vid=4&sid=093e0f57-b70b-4d96-a682-e424d8684c34@sdc-v-sessmgr02.

 

Appendix

1. 10	2. 7	3. 2	4. 8	5. 3	6. 12	7. 7	8. 5	9. 9	10. 7
11. 9	12. 11	13. 11	14. 7	15. 4	16. 7	17. 4	18. 6	19. 11	20. 4
21. 7	22. 7	23. 6	24. 4	25. 7	26. 11	27. 6	28. 9	29. 3	30. 8
31. 3	32. 8	33. 10	34. 3	35. 7	36. 9	37. 11	38. 10	39. 9	40. 8
41. 6	42. 9	43. 9	44. 10	45. 8	46. 8	47. 9	48. 9	49. 5	50. 10
51. 7	52. 10	53. 7	54. 9	55. 10	56. 9	57. 7	58. 11	59. 8	60. 3
61. 8	62. 4	63. 5	64. 4	65. 8	66. 6	67. 5	68. 6	69. 9	70. 10
71. 2	72. 4	73. 3	74. 6	75. 6	76. 5	77. 7	78. 11	79. 9	80. 3
81. 9	82. 6	83. 6	84. 9	85. 12	86. 3	87. 5	88. 6	89. 10	90. 8
91. 9	92. 4	93. 6	94. 7	95. 3	96. 8	97. 10	98. 4	99. 2	100. 5

 

These are the sums I recorded after rolling two dice 100 times.