Reaz Shakil

Date:10/22/2019

Writing for Engineering

 

Dice Rolling is it Random:

The Probability of Rolling Pair of Dice.

 

 

Abstract:

 

The Dice rolling experiment allows persons to understand how probabilities work. The Idea of this experiment is to roll a pair of dice for a hundred times and record the data for each trail. The person that experimented by collecting all the data he or she had to determine something that they want to prove from the data. I created a program which is to compute the rolling of pair of dice 100 times. I collected the data from the experiment and calculated the percentage of probabilities of the sum. Since this, a probability experiment will not be accurate all the time, because randomizing but the probabilities of getting seven in the rolling dice experiment are higher than every other number.

 

Introduction:

The rolling a pair of dice is looks random but it not if you think by using probabilities you can have a close and most accurate guess. The probabilities by definition is chance of something will happen. The idea is to roll a pair of dice 100 times in this case I did not use dice to collect data I created a program which allows me to simulated pair of dice generate number for 100 trails. Normally the pair dice would have one to six numbers on each many people believe that by rolling dice they would have equal chances of getting outcome however that is not true since the dice has 6 sides that mean 36 different number arraignment but only 11 are the combined outcome. For instance, the number 7 has many combined numbers 6 different pairs of dice see figure 3. 7 is the most Possibilities of the outcome from 11 numbers combined because seven has three different ways to be generated from rolling a pair of dice. Therefore, my hypothesis would be the number seven would repeat the most.

Materials:

• 2 Dice in my case I created program which generate sum of two dice
• Paper and Pencil
• Computer

Methods:

• Roll a pair of dice and record the data each trial
• Repeat 100 times or type 100 times in pair of dice generator
• Calculate the sum of each trial.

Result:

 

Figure 1: This is a pie graph show the percentage of sum which repeated out of 100 trials.

Figure 2: This is a bar graph which shows the sum of all combine numbers of dice.

Total on dice	Pairs of dice	Probability
2	1+1	1/36 = 3%
3	1+2, 2+1	2/36 = 6%
4	1+3, 2+2, 3+1	3/36 = 8%
5	1+4, 2+3, 3+2, 4+1	4/36 = 11%
6	1+5, 2+4, 3+3, 4+2, 5+1	5/36 = 14%
7	1+6, 2+5, 3+4, 4+3, 5+2, 6+1	6/36 = 17%
8	2+6, 3+5, 4+4, 5+3, 6+2	5/36 = 14%
9	3+6, 4+5, 5+4, 6+3	4/36 = 11%
10	4+6, 5+5, 6+4	3/36 = 8%
11	5+6, 6+5	2/36 = 6%
12	6+6	1/36 = 3%

 

Figure 2: This table shows the probabilities of each of the combine number percentage.

Analysis:

After the experiment I can say that my hypotheses were wrong because it’s bell curve graph it not 100% accurate tell the probability of which number would repeat the most. There are odd in each of the number people can easily eliminate the number what would list repeat for example number 2 and 12 are the one has the lowest chance of repeating (see figure 3). In the data that I collected which shows a pattern combine number that has the lowest combine number appear less. For instance, if you look at figure three you will see the probabilities of getting each of the combine numbers are not that apart from my experiment result. The number one to four and ten to twelves is almost same. It started to change in the middle but there is still a pattern between each of the number in figure two number six and nine was repeated equally and number seven and eight was equally repeated it looks like mirror reflection where the numbers are behaving accordingly. Of course, if I were do more trials It would be different; the result would be more accurate and eliminated chance of the random numbers appearance.

 

Nevertheless, there were another similar study was about rolling dice simulation the experiment was done by computer as well. According to the article “Investigation of probability distributions using dice rolling” throughout the simulation they experiment up to 5000 times three dice roll. Even though they did an experiment which was 50 times greater than mine and extra dice was simulated, but the outcome was very similar. Our graph is bell curved and almost all the result is same. No matter the odds the probability will give an pattern which will allow a person to have more precise number because of the probability many people call number seven is the lucky number and if you look at figure three the number seven has the highest percentage in the probability of a pair of dice.

Conclusion:

I can say that this experiment was not as I expected to be my hypothesis were wrong however the experiment was not that surprising since the probabilities of pair of dice is bell curve. My experiment after I analyzed the results it was very similar to the bell curve graph there were small difference due to lack of trials. In order for me to get an accurate result I need to do more trials as I stated earlier by doing it so it will help me to doge any number that could’ve been random; as result I would have more accurate result very similar to the figure 3 result.

Work Cited Page:

Lukach, S., & Engel, R. (2010). Investigation of probability distributions using dice rolling simulation. Australian Mathematics Teacher, 66(2), 30–35. Retrieved from https://search-ebscohost-com.ccny-proxy1.libr.ccny.cuny.edu/login.aspx?direct=true&db=a9h&AN=51533174&site=ehost-live

Appendix:

Figure 5:

DicePercent = 0.0

Dice1 = 0

Dice2 = 0

Rolls = 0

# Display name of program, any instructions

print(“Winning at Dice? \nRoll two dice, sum the values on the upper faces.”)

# Input: assumed values, values provided by user

Rolls = int(input(“How many times do you want to roll the dice?”))

print(“\n”)

# Processing: carry out calculations

import random

for index in range(Rolls):

Dice1 = random.randint(1,6)

Dice2 = random.randint(1,6)

k=Dice1+Dice2

print(“Roll #” + str(index+1) + ” First dice = ” + str(Dice1) + ” Second dice = ” + str(Dice2)+”, sum= “+str(k))

print(“\nTwo Dice Rolled ” + format(Rolls, ‘,d’) + ” times.”)

 

 

 

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