Exploring the probability of rolling a pair of dice: A lab report on Dice Probability
Abstract:
The objective of this experiment is to determine how probable a particular sum of dice could be when they are rolled together and how frequent it is by rolling two dice 100 times and analyzing the data obtained. The data I obtained in this data doesn’t seem to specifically point out one particular sum which was more likely to come out than others. This experiment’s data can be used to further show if probability works, especially regarding the sequencing and frequency of a specific event.
Student Name: Nusrat Patwary
Date: 03/21/2019
Introduction
Get a pair of dice and roll them to get the nearest probability. Probability means that the chance of something will happen and more likely an assumption that same event or pattern will happen. A very good way to understand the probability is by looking at outcomes throw of a die. There is six side of a die, so for each trial there is six possible outcomes by rolling a die. In this particular experiment, we were looking for the sum of the probability by rolling two dice for 100 times. Before the experiments, I made hypothesis that probability is not absolute and the frequency at which a specific events occurs may vary due to unknown environmental factors, since probabilistic events do not necessarily follow a sequence.
Materials
- A pair of dice
- A flat surface area
- Pen and paper
- Data table
Methods
- I rolled a pair of dice 100 times.
- Wrote down all the all the outcomes in a notebook.
- For each trial I added the outcome of die1 and die2 (D1+D2).
- Calculated the number of given sum appeared after rolling dice 100 times.
- Used excel sheet to draw the graph.
Results
By looking at the graph, we can say that the sum of the probability in not absolute. It’s may vary in different experiments, because by rolling the dice we get random numbers, it doesn’t follow any specific pattern.
Analysis
The purpose of my this experiment is to find out that probability is no absolute. By rolling the dice you can get get any number, sometimes you may get same pattern again and again and sometimes not this why its call probability. There is no surety that the you will get same outcomes. To get the nearest probability you can roll a pair of dice as much as you can. To prove my hypothesis right or wrong I rolled a pair of dice 100 times. By doing this experiment I found that the results may vary, and its do not always follow sequence. One experiments is not enough to draw the conclusion so I compared my experiment result with another research source call mathworld about dice probability. Comparing both experiment I found that the sum of the probability is not absolute. The sum of the some numbers can be appear more often than others.
Conclusion
probability is not absolute and the frequency at which a specific events occurs may vary due to unknown environmental factors, since probabilistic events do not necessarily follow a sequence. Based on my experiment, I can say that my hypothesis is correct. As you can clearly see the results that the sum of time some number are more that others, some same, some numbers were appeared more than other and its dont follow any specific pattern or sequence. So, one should not follow this data to make any conclusion, because probability is not absolute and data you get it’s just random numbers you can you rolling dice.
Citation weisstein, Eric W. “dice.” from MathWorld- A wolfram web resource. http://mathworld.wolfram.com/Dice.html
Long Data Set
| Number of rolling | Dice # 1 | Dice # 2 | sum | Number of rolling | Dice # 1 | Dice # 2 | sum |
| 1 | 1 | 1 | 2 | 20 | 5 | 3 | 8 |
| 2 | 3 | 1 | 4 | 21 | 4 | 2 | 6 |
| 3 | 4 | 6 | 10 | 22 | 5 | 5 | 10 |
| 4 | 4 | 3 | 7 | 23 | 3 | 5 | 8 |
| 5 | 5 | 5 | 10 | 24 | 6 | 1 | 7 |
| 6 | 1 | 4 | 5 | 25 | 1 | 1 | 2 |
| 7 | 6 | 6 | 12 | 26 | 1 | 1 | 2 |
| 8 | 5 | 2 | 7 | 27 | 5 | 6 | 11 |
| 9 | 2 | 2 | 4 | 28 | 6 | 6 | 12 |
| 10 | 4 | 4 | 8 | 29 | 4 | 6 | 10 |
| 11 | 3 | 5 | 8 | 30 | 5 | 1 | 6 |
| 12 | 1 | 1 | 2 | 31 | 5 | 5 | 10 |
| 13 | 5 | 45 | 10 | 32 | 4 | 5 | 11 |
| 14 | 6 | 6 | 12 | 33 | 4 | 4 | 8 |
| 15 | 3 | 6 | 9 | 34 | 2 | 1 | 3 |
| 16 | 2 | 1 | 3 | 35 | 5 | 3 | 8 |
| 17 | 6 | 6 | 12 | 36 | 5 | 6 | 11 |
| 18 | 6 | 6 | 12 | 37 | 6 | 6 | 12 |
| 19 | 3 | 4 | 7 | 38 | 4 | 2 | 6 |
| 39 | 2 | 2 | 4 |
| Number of rolling | Dice # 1 | Dice # 2 | sum | Number of rolling | Dice # 1 | Dice # 2 | sum |
| 40 | 3 | 1 | 4 | 64 | 3 | 4 | 7 |
| 41 | 4 | 6 | 11 | 65 | 2 | 3 | 5 |
| 42 | 3 | 4 | 7 | 66 | 5 | 5 | 10 |
| 43 | 2 | 5 | 7 | 67 | 6 | 4 | 10 |
| 44 | 1 | 4 | 5 | 68 | 5 | 5 | 10 |
| 45 | 4 | 5 | 9 | 69 | 6 | 3 | 9 |
| 46 | 2 | 1 | 3 | 70 | 3 | 1 | 4 |
| 47 | 5 | 6 | 11 | 71 | 2 | 2 | 4 |
| 48 | 3 | 3 | 6 | 72 | 4 | 6 | 10 |
| 49 | 2 | 4 | 6 | 73 | 6 | 5 | 11 |
| 50 | 2 | 4 | 6 | 74 | 5 | 4 | 9 |
| 51 | 6 | 3 | 9 | 75 | 5 | 6 | 11 |
| 52 | 6 | 4 | 10 | 76 | 5 | 6 | 11 |
| 53 | 1 | 1 | 2 | 77 | 1 | 2 | 3 |
| 54 | 3 | 4 | 7 | 78 | 3 | 2 | 5 |
| 56 | 2 | 3 | 5 | 79 | 5 | 2 | 7 |
| 57 | 5 | 3 | 8 | 80 | 6 | 5 | 11 |
| 58 | 4 | 4 | 8 | 81 | 3 | 4 | 7 |
| 59 | 2 | 3 | 5 | 82 | 2 | 1 | 3 |
| 60 | 5 | 4 | 9 | 83 | 6 | 6 | 12 |
| 61 | 6 | 1 | 7 | 84 | 5 | 2 | 7 |
| 62 | 1 | 3 | 4 | 85 | 2 | 2 | 4 |
| 63 | 6 | 5 | 11 | 86 | 5 | 3 | 8 |
| Number of rolling | Dice # 1 | Dice # 2 | sum | Number of rolling | Dice # 1 | Dice # 2 | sum |
| 87 | 5 | 6 | 11 | ||||
| 88 | 4 | 4 | 8 | ||||
| 89 | 6 | 4 | 10 | ||||
| 90 | 4 | 1 | 5 | ||||
| 91 | 1 | 1 | 2 | ||||
| 92 | 5 | 5 | 10 | ||||
| 93 | 5 | 1 | 6 | ||||
| 94 | 1 | 6 | 7 | ||||
| 95 | 2 | 1 | 3 | ||||
| 96 | 6 | 3 | 9 | ||||
| 97 | 6 | 5 | 11 | ||||
| 98 | 2 | 4 | 6 | ||||
| 99 | 3 | 1 | 4 | ||||
| 100 | 2 | 2 | 4 |
