Probability Lab Report

 

It’s not uncommon to find people believing that if an individual accomplishes something a few times, they will get indistinguishable outcomes if they were to conduct the same activity multiple times, regardless of the amount. As a matter of fact, it is quite different  than just to expect the same outcome over and over again; and this report will explain and explore that concept using dice. One hundred of them to be exact. 

In terms of rolling a pair of six sided dice, the possible outcomes are more than just the two faces that is face up, because in reality, that outcome for a single pair of dice is only one out of thirty-six. How did we achieve this number?. Well when you roll a die, you get one face out of six (1 / 6) , therefore, if you are to roll two dice, you will have to square that: (1 /6) x (1 / 6) = 36 possible outcomes. That being said, picturing this on a grander scale of one hundred dice, and the mind goes crazy trying to figure out the possible outcomes. 

In this lab report, we will see the possible outcomes of rolling one hundred dice, and in terms of analysis, we will be using a set goal of counting the number of times a pair of dice adds up to seven when rolled fifty times. In terms of prior knowledge, it is important to know the concept of theoretical probability. By definition, “theoretical probability is the number of ways a favorable event can occur versus the amount of possible ways a thing can occur”. The simplest and most easy to understand example would be flipping a coin, and as we know a coin have 2 sides, so the theoretical probability behind flipping a coin is 50-50 (50%). 

Theoretical probability however, differs from another concept called experimental probability. By definition, experimental probability simply means the amount of times something occurs when compared to the total amount. For example, going back to the coin example, if you are to choose heads and flip a coin ten times resulting is four heads. Then the experimental probability  is 4:10, which is 40%. The best way to remember experimental probability is as a ratio.

HYPOTHESIS

In my thought process, I am considering that since I will be rolling 10 dice at a time, the probability of getting a pair that adds up to 7 is higher instead of rolling a pair hoping it adds to seven; therefore the chance of getting more than one pair is there. I predict for every 10 dice rolled, there will be at least 3 pairs that adds up to seven.        

 

MATERIALS

• 10 dice
• Notepad and pencil
• Flat even surface such as a table top
• Calculator
• Plastic cup

 

 METHODS

1.  Place 10 dice in a cup. 
2. Place hand over cup to avoid any falling out while shaking.
3. Shake thoroughly until satisfied dice are mixed up.
4. As you are coming to an end, remove your hand over the cup.
5. Tilt cup so all the dice falls on the flat even surface at random.
6. Count the number on every face, and log them down.
7. Calculate which two numbers out of the set of ten sums up to seven.
8. Log down the amount of pairs counted.
9. Add the total number of pairs and divide by 100 in order to find a percentage. 

 

RESULTS

Results From Rolling 10 Dice Simultaneously/Average	Numbers 0f Paired Combinations Equaling To 7	Combinations
1 – 2 – 1 – 4 – 2 – 4 – 4 – 2 – 6 – 3 (Avg: 2.9)	2	1 / 6, 4 / 3
5 – 4 – 3 – 3 – 1 – 3 – 6 – 2 – 3 – 3 (Avg: 3.3)	3	5 / 2, 4 / 3, 1 / 6
3 – 1 – 6 – 1 – 2 – 2 – 1 – 3 – 1 – 1 (Avg: 2.1)	1	1 / 6
4 – 1 – 1 – 2 – 2 – 6 – 5 – 2 – 3 – 4 (Avg: 3.0)	3	4 / 3, 1 / 6, 5 / 2
3 – 6 – 1 – 4 – 1 – 5 – 1 – 5 – 3 – 4 (Avg: 3.3)	2	6 / 1, 4 / 3
6 – 6 – 4 – 5 – 4 – 6 – 3 – 1 – 2 – 1 (Avg: 3.8)	4	1/ 6, 1 / 6, 4 / 3, 5 / 2
3 – 2 – 2 – 5 – 5 – 5 – 3 – 1 – 1 – 1 (Avg: 2.8)	2	5 / 2, 5 / 2
4 – 5 – 6 – 6 – 1 – 4 – 1 – 2 – 6 – 3 (Avg: 3.8)	4	4 / 3, 5 / 2, 6 / 1, 6 / 1
2 – 3 – 1 – 3 – 1 – 4 – 4 – 3 – 5 – 2 (Avg: 2.8)	3	3 / 4, 3 / 4, 5 / 2
4 – 5 – 6 – 3 – 2 – 2 – 4 – 2 – 5 – 3 (Avg: 3.6)	4	4 / 3, 4 / 3, 5 / 2, 5 / 2
(Total Avg. For 100 Rolls: 3.14)	(Total Avg. Of Pairs Equaling 7 For 100 Rolls:  28 % )	28 Pairs

 

ANALYSIS

In terms of timing, it wasn’t difficult getting through all one hundred rolls considering I rolled ten dice (5 pairs) at a time. From the results, we see that there are no clear pattern. In addition, in a roll of 10 dice, no rolls had any similarities compared to any other. What is clear however, is the pairs adding up to seven is relatively similar in for every 10 dice rolled. The number of pairs never exceeded four, and rarely fall under two, all but one. There was three cases of 2 pairs, three cases of 3 pairs, and three causes of 4 pairs out of 10 rolls. This is in correlation to another experiment done by Reese Kostka, who found a 16 ⅔ % theoretical result out of 50 trials, which in theory for my experiment which is 100 trials, would be 33 ⅓ % when the amount of trials is doubled (50 trials = 16 ⅔ %, therefore 100 trials should be around 33 ⅓ %). Kostka’s experiment is cited below.  My experiment produced 28% out of 100 trials.

 

CONCLUSION

When all is said and done, the results clearly if not confirms, then surely supports my hypothesis that for every ten dice rolled, there will be at least 3 pairs that adds up to seven. Which is somewhat the median of the set of data, sharing the spotlight with pairs of 2, and pairs of 4, but not pairs of 1 or anything higher than pairs of 4. Which is generally in the same range of value I predicted. 

 

Similar Lab Report found online. Attached at the back. 

(since this is a private upload, it is very difficult getting an MLA citation, therefore i will provide a link as well as a hard copy.)

http://reesekostka.weebly.com/uploads/3/9/0/0/39005063/probabilitylabreport.pdf