Lab Report

“Which Number of the Sums Will Appear the Most?”

Roll A Dice For A Hundred Times

Xiaozhi Zhu

10/30/2018

 

Abstract:

In this rolling a pair of dice experiment, I used two dice to see what’s the result going to be after rolling the dice 100 times, I want to use this experiment to know which number of sums will occur and appear the most. In this experiment, I used a random website named, “rolling dice generator”, to collect the statistics of the sums in the numbers, however, according to the datas on the bar graph, I came up with a conclusion that number 7 is the number of the sums which appears the most during this experiment. Although the number seven appeared the most in my experiment, but to get a very representative and authoritative test result base on this experiment, then many experimental attempts are necessary.

 

Introduction:

First of all, the purpose of this experiment is actually to roll a pair of dice for 100 times, and secondly to get the sum of the most frequently occurring numbers. But in a nutshell, the probability of the sum of the numbers obtained from this experiment are very broad because the dices in this experiment are each composed of faces of six different numbers. The probability of a number appearing in a dice is between the numbers from 1 to 6, but if there are two dice, then it has to consider more possibilities. For example, a dice is a set of numbers from 1 to 6, then two dice are 2 to 12. But each dice has six different faces, so this increases the complexity of this experiment because there are six different results come from each test, and this will have at least a hundred different results. Even though based on the experiment that 7 is the number appears the most, but I assume the probability that the number is greater than 6 will be higher than the probability that the number is less than 6.

 

Method & Materials:

 

• Rolling dice generator

 

• Bar graph (Statistic of rolling dice)
• Percentage calculator

During this rolling dice experiment, I recorded the probability of occurrence from the numbers 1 to 12 by using the “Rolling dice generator”, and then I recorded those data in detail using the bar graph because that’s the easiest and simplest way to show the result of statistics and probability in this experiment. In addition, I used a percentage calculate to calculate that how likely each number will appear, and the data of the probability collected by this method can tell me which a number of sums have the highest probability.

Result:

Figure 1

The frequency on figure 1 the bar graph is the number of occurrences of the sum of each number, and that’s the variable in this experiment and it can be changed based on the experiment. However, the total number of rolls are 100 times and the number from 2-12 are invariant in this experiment, they can not be changed. The frequency also means probability in this case, which shows the which sums of the number will appear the most.

 

Analysis:

After I finished the experiment of rolling the dice 100 times. I got an accurate result, which that is the number 7 is the most frequent occurrence. In so many time of experiments, it has appeared up to 19 times. Of course, the numbers 6 and 8 have also appeared many times, and they appear 14 and 16 times in total. As my hypothesis has mentioned, the probability that the number is greater than 6 will be higher than the probability that the number is less than 6 because there are so many different ways that we can get the numbers which are greater than 6 or 7 or 8 but less way to obtain the smaller numbers. For example, there are six different ways in total to get the number sum of 7, such as 1+6, 2+5, 3+4, 6+1, 5+2, 4+3, but for numbers like 2, or 3, there are probably only one or two ways to get them, such as 1+1 is equal to 2, and 1+2=3, 2+1=3.

Furthermore, the article I found called, “Two-dice horse race”, written by Colin Foster and David Martin, which directly proves to me that my hypothesis is correct because the results of their experiments have drawn very similar conclusions with my experiment, which the sum of the numbers in the middle of a set, is usually and most likely occurs the most, there is no exception in their experiment too.

 

Conclusion:

Based on the fact that my rolling dice experiment has proved, the number of sums which appear the most is 7. At the same time, my experimental results and pre-experimental assumptions (the hypothesis) are quite similar to those of other writers. So this can indirectly prove the accuracy of my experimental results and while making it more credible. The experiment was done entirely through the computer, however, this experiment does not represent the credibility of all the dice experiments because my experiment is based solely on my own data and the results obtained from this experiment and it does not represent the result in fact of all the dice experiments. In order to get a very representative and authoritative test result base on this experiment, then many experimental attempts are necessary.

 

Work Cited & Reference:

1. Foster, C., & Martin, D. (n.d.). Two-dice horse race. Retrieved May 20, 2016, from https://web-a-ebscohost-com.ccny-proxy1.libr.ccny.cuny.edu/ehost/detail/detail?vid=3&sid=204e660d-63cd-4dc5-9c84-082c0fa6de65@sdc-v-sessmgr02&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ==#AN=117147864&db=a9h