Suatcan Isik

October 23, 2019

ENGL 10200

Better Pick Seven: Probability of Dice Roll, Lab Report

 

Abstract

Which number is the highest chance to get when you roll 2 dices? How can you calculate the theoretical and experimental percentage of numbers that we get from rolling dices? In this experiment, you will see all the combinations that can be find by rolling 2 dices. Theoretical and experimental results will prove that one of the numbers is more common than other numbers. You will see why the most common number is 7 when you roll 2 dices.

 

Introduction

This dice experience will help us prove that the probability of numbers that we can get by rolling the dice. However, some of the numbers come up more frequently than other numbers. As in hypothesis, 7 has the highest percentage of coming up after rolling dice because it has the highest number of different combinations. With the experimental method, we will test this theory by rolling the dice 200 times.

 

Materials and methods

In this experiment, we will look at the dice in two different methods and we will examine their similarities. The first method that we will use is theoretical, which will allow us to find out all the combinations that can come up by rolling the dice and will help us to find out about their probability. On the second method, we will roll the dice 200 times and as of the first method, we will find their frequency and percentage of coming up. Then we will investigate their differences and similarities with graphs. Then we will prove the hypothesis and conclude the theory.

Theoretically, 1 dice has 6 sides which give it 6 different combinations. However, rolling 2 dice makes it gives so many more combinations. If we calculate we get 36 different outcomes. We will calculate every combination, even 2,3 and 3,2 because getting the same numbers doesn’t change the fact of their percentage. Even though 2,3 and 3,2 do look so same, they are not the same combinations. They both different combinations that have the same percentage of coming out. So, we will find all the possibilities and graph our records down.

On the experimental method, we don’t need to calculate anything, we are just going to roll the dice and record results then put them on a table graph as we see in Figure1 and look at their difference between theoretical results.

Results

As we can see through Figure 1, 7 has 6 different combinations out of 38. Which gives it an almost 16% chance to roll, theoretically. On the other side, lower or higher numbers than 7 have a lesser number of combinations as 5, 4, 3 and 2. Which lowers their percentage to 13%, 10.5%, 8% and 5%.

Even though we can find their percentage of coming up, we still can’t really predict what might come up, when we roll dices. So, when I roll dices 100 times, I came up with more 9s than 7s. I increased the number of trials to get a more accurate percentage for the experimental method. As I roll dices more and more, experimental data got closer to the theoretical data. So, we can assume that even though we don’t have the same results but similar to each method, increasing the number of trials on the experiment method will make get closer to the theoretical results.

 

	Theoretical			Experimental Results
	Combinations	Number of combinations	Percentage %	Number of Results	Percentage %
2	(1,1)(1,1)	2	5.263	2	1
3	(1,2)(2,1)	2	5.263	7	3.5
4	(1,3)(3,1)(2,2)	3	7.895	12	6
5	(1,4)(4,1)(2,3)(3,2)	4	10.526	19	9.5
6	(1,5)(5,1)(2,4)(4,2)(3,3)	5	13.158	34	17
7	(1,6)(6,1)(2,5)(5,2)(3,4)(4,3)	6	15.789	42	21
8	(2,6)(6,2)(3,5)(5,3)(4,4)	5	13.158	24	12
9	(3,6)(6,3)(4,5)(5,4)	4	10.526	29	14.5
10	(4,6)(6,4)(5,5)	3	7.895	19	9.5
11	(6,5)(5,6)	2	5.263	7	3.5
12	(6,6)(6,6)	2	5.263	5	2.5
	Total:	38	100%	200	100%

Figure 1

 

As we can see more clearly in Figure 2, the frequency of both methods is following the same pattern as they get closer to 7. Their percentage is increasing as they get to 7, then they start decreasing after they reached the highest percentage, which is 7.

Figure 2

 

Analysis

So, we can assume that the probability of getting 7 as the addition of 2 dices, is proven by our experimental and theoretical methods. We will also check another journal article about rolling dices. In the “A Second-Grade Probability and Graphing Lesson” article, the teacher gives children dice for them to roll and write their experimental results. While using dices, they also get a similar result. According to the graph, they drown in the article we can say that their experimental results are mutual.

The graph that students colored blue for each addition they get by rolling dices:

Figure 3

Conclusion

We can conclude that 7 is the most common number that you can get by rolling the dice. Because combinations that give the seven is more than the other numbers that you can get. As we can see in Figure 1, 7 has a 15% chance with 6 different combinations. On the other hand, rest combinations have 13, 10, 7 or 5% of chance to get by while rolling the dice. Experimental research also follows similar results. Even though I couldn’t get right about results when I roll 100 times, increasing the experiment gives more accurate results as can be seen in Figure 1, 7 has 21% of showing up and the rest decreases. Also in Figure 2 we can see that not only they follow the number 7 but other numbers percentage also follows the same pattern.

 

Works cited list

Woodward, Ernest. “A Second-Grade Probability and Graphing Lesson.” Arithmetic Teacher 30.7 (1983): 23-24. Web.

 

Appendix:

Sample Calculation:

 

Dice Rolls for Experimental Method:

54,53,52,52,13,33,12,36,36,65,65,15,23,31,55,65,53,66,53,63,

42,16,54,42,52,55,66,56,26,33,61,51,15,22,12,55,45,46,35,24,

24,41,36,14,65,34,46,54,52,23,51,45,62,55,66,35,52,35,65,36,

34,41,12,23,24,64,35,45,25,36,62,46,41,46,61,33,52,45,63,56,

24,14,43,45,64,41,36,22,14,43,53,41,64,54,52,46,33,45,13,26,

61,25,34,45,43,54,66,46,25,62,44,21,42,33,43,33,61,45,64,11,

16,33,23,23,45,12,26,33,33,32,35,43,45,46,35,51,24,34,63,13,

62,15,23,51,45,62,51,53,16,11,25,25,25,46,54,35,55,13,25,35,

45,15,63,34,34,23,15,46,22,66,23,33,34,21,62,61,61,53,41,34,

55,54,12,24,51,42,22,31,31,25,63,52,26,52,33,64,15,61,16,11

 

Sum of Rolls for Experimental Method:

9,8,7,7,4,6,3,9,9,11,11,6,5,4,10,11,8,12,8,9,

6,7,9,6,7,10,12,11,8,6,7,6,6,4,3,10,9,10,8,6,

6,5,9,5,11,7,10,9,7,5,6,9,8,10,12,8,7,8,11,9,

7,5,3,5,6,10,8,9,7,9,8,10,5,10,7,6,7,9,9,11,

6,5,7,9,10,5,9,4,5,7,8,5,10,9,7,10,6,9,4,8,

7,7,7,9,7,9,12,10,7,8,8,3,6,6,7,66,7,9,10,2,

7,6,5,5,9,3,8,6,6,5,8,7,9,10,7,6,6,7,9,4,

8,6,5,6,9,8,6,8,7,2,7,7,7,10,9,8,10,4,7,8,

9,6,9,7,7,5,6,10,4,12,5,6,7,3,8,7,7,8,5,7,

10,54,3,6,6,6,4,4,4,7,9,7,8,7,6,10,6,7,7,2