Rolling a pair of dice and their probable outcomes

 

    Abstract:

 

 Rolling of dice gives us different outcomes each time we roll it and the outcome is certain from 1 to 6. However, if we add another dice with the experiment, rolling them will give random numbers by adding both dice’s outcomes. The outcome, in other words, the sum of two dice rolling is probable. There is no pattern will be seen while dice are rolling. Each rolling session we will get different numbers. In that case, the most recurrent number I got was seven. Every rolling session I got a random number however, seven was the most frequent number and there is no pattern was noticed during this experiment.

 

Anik Das

October 22, 2019

 

Introduction

Probability refers that something will happen within the given choice. It is a mathematical tool to make decisions when there is uncertainty. The greater probability means the more likely to occur. If we roll one dice we can get a random number between 1,2,3,4,5,6. However, adding another dice will increase the sum of the outcome than rolling one dice. Let’s say we are rolling two dice simultaneously then we will get two different numbers, which means that for the first dice with number 1 we can get 1,2,3,4,5,6 and so for 2,3,4,5 and 6. 

	1	2	3	4	5	6
1	1,1	1,2	1,3	1,4	1,5	1,6
2	2,1	2,2	2,3	2,4	2,5	2,6
3	3,1	3,2	3,3	3,4	3,5	3,6
4	4,1	4,2	4,3	4,4	4,5	4,6
5	5,1	5,2	5,3	5,4	5,5	5,6
6	6,1	6,2	6,3	6,4	6,5	6,6

 

This table is giving the idea of probability from rolling of two dice where we can see the most frequent number happening is 7 from the 36 different combinations. If we add the numbers from the bottom left corner to the top right corner of the table diagonally we will get seven as the most recurrent number. 

 

Materials and Procedure:

The materials that I have used for this experiment were just two different colored dice. The outcome from the rolling was recorded on a spreadsheet. A total of 100 was taken to do this experiment and two dice were rolling simultaneously for each attempt.

 

Results:

We know from the top table that the most frequent number is 7. However, because of the insufficient trial, we have gotten a  skewed result. Based on the graph, 8 is the most frequent number, where the table I wrote on the top says that it will be 7. To fix this confusion we need more trial than 100 times.

Trial no	dice no 1	dice no 2	sum of the two dice
1	4	1	5
2	4	4	8
3	3	1	4
4	6	3	9
5	1	3	4
6	3	2	5
7	6	3	9
8	6	5	11
9	4	4	8
10	2	2	4
11	2	1	3
12	3	4	7
13	6	2	8
14	6	1	7
15	5	3	8
16	3	1	4
17	6	1	7
18	5	4	9
19	6	3	9
20	2	1	3
21	4	4	8
22	5	4	9
23	5	3	8
24	6	4	10
25	6	2	8
26	6	5	11
27	5	1	6
28	6	4	10
29	2	2	4
30	4	3	7
31	3	1	4
32	5	5	10
33	3	1	4
34	6	1	7
35	1	6	7
36	6	3	9
37	3	3	6
38	6	4	10
39	2	1	3
40	4	4	8
41	6	2	8
42	5	1	6
43	5	3	8
44	6	2	8
45	3	3	6
46	6	4	10
47	4	4	8
48	6	1	7
49	2	1	3
50	6	6	12
51	2	5	7
52	6	6	12
53	2	5	7
54	5	2	7
55	6	5	11
56	5	2	7
57	6	6	12
58	3	5	8
59	5	6	11
60	3	6	9
61	5	4	9
62	5	2	7
63	4	6	10
64	5	2	7
65	5	5	10
66	2	4	6
67	6	5	11
68	3	5	8
69	5	1	6
70	1	4	5
71	6	3	9
72	3	5	8
73	2	2	4
74	5	3	8
75	6	5	11
76	2	1	3
77	1	5	6
78	6	3	9
79	3	2	5
80	2	2	4
81	1	6	7
82	3	3	6
83	5	4	9
84	2	1	3
85	1	1	2
86	5	6	11
87	2	5	7
88	4	5	9
89	6	4	10
90	6	2	8
91	5	4	9
92	2	3	5
93	5	4	9
94	2	2	4
95	6	4	10
96	3	2	5
97	5	3	8
98	3	1	4
99	3	2	5
100	5	2	7

 

Discussion

The result we got from the pie chart and also based on the table was unexpected. Because of the small sample size, in other words, the insufficient trial number we got a different answer. If we could go more than 100 times, we could get a precise answer which is 7. According to the writer in the text, it says that adding more dice in the experiment would give us more precise information which means we would get more binomial distribution and which will look like a bell curve. We don’t have any influence on the outcome of the rolling dice. However, the bigger sample size might change the most recurrent number that we can get.

 

Reference:

BAKER, J. D. Rolling the Dice. Mathematics Teacher, [s. l.], v. 106, n. 7, p. 551–556, 2013. Disponível em: <https://search-ebscohost-com.ccny-proxy1.libr.ccny.cuny.edu/login.aspx?direct=true&db=a9h&AN=88796493&site=ehost-live>. Acesso em: 23 out. 2019.