MATH201 – What are the Chances Assignment – Devin Sloan
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Bryant & Stratton College *
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Course
201
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
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3
Uploaded by brownsugah31
Module 5 - What are the chances? Assignment Template
Use a six-sided die and what you have learned so far in your course to help you answer the questions below. If you do not have a die to use at home, you can use the virtual die via the link below. Virtual Six-Sided Die 1.
In 150 words, describe the difference between theoretical
and experimental
probability. Which do you think is more reliable and why?
When it comes to probability, there are two kinds: experimental and theoretical. Because experimental probability is based on actual experiment results, it is an extremely trustworthy method for determining the possibility of an event occurring. By assessing the potential possibilities of the experiment, we may compute the probability of an event occurring. The experimental probability is calculated using a simple and effective procedure that involves calculating the ratio of the number of times a specific event occurred to the total number of trials done. In general, experimental probability is a crucial technique for accurately estimating the probability of an event occurring based on empirical data. The formula used to calculate theoretical probability and experimental probability differs. Since it involves carrying out experiments and getting data from actual situations, experimental probability is a more trustworthy approach of gathering probability information. On the other hand, theoretical probability is less precise because it just makes assumptions about possible outcomes. Although it is calculated using mathematical concepts, actual experimentation is not taken into account. Rather than through experimentation, assumptions are used to calculate theoretical probability.
These assumptions are used to quantify the likelihood of an event happening, allowing for a reliable assessment of the likelihood without doing an actual experiment. The number of desired outcomes must be divided by the total number of possible outcomes in order to calculate probability. Because experimental probability uses actual facts rather than conjecture, it is more accurate.
2.
Determine the theoretical probability
of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction
, a decimal
(rounded to three places) and a percentage
(rounded to one decimal place).
One normal die has six possible outcomes; hence the following is the theoretical result: Fraction: 1/6 Decimal: 0.167 Percentage: 16.7%
3.
Now, take your die and roll it the number of times that is equal to your age in years. Create a table below to document each roll of the die. Use this trial data to determine the experimental probability
of rolling a two on the die. Write this probability in three equivalent forms: as a fraction
, a decimal
(rounded to three places) and a percentage
(rounded to one decimal place).
5
4
5
3
6
2
4
2
3
6
4
6
2
3
5
4
2
3
3
Because the two was rolled four times out of a possible 19 times, the experimental Probability is determined as followed:
Fraction: 4/19 Decimal: 0.211 Percentage: 21.1%
4.
Was your experimental probability
equal to the theoretical probability
of rolling a two? If not, do you think the two calculations would be closer if you doubled the number of times you rolled your die? Explain in 200 words.
The theoretical likelihood of rolling a two is lower than the experimental possibility. If we rolled the die twice as often, the computations would be more precise. The law of large numbers, which states that if an experiment is repeated numerous times, the experimental probability will converge toward the theoretical probability, can be used to explain this phenomenon. Because only one of the six numbers on a regular die is a 2, there is a chance that the number that appears on the top face will be 2. Therefore, there is a 16.7% theoretical chance of rolling a two. The odds of getting more than one "2" or none at all when rolling a die six times
deviate from the predicted probability. I conducted an experiment by throwing the die 19 times, and I received four "2"s. As a result, as opposed to the predicted probability of 16.7%, our experimental probability was higher at 21.1%. The experiment's use of chance can be used to explain the difference between the two probabilities. However, if 600 tosses are conducted, the relative frequency of each outcome should be quite close to the theoretical probability. The estimated frequency of the result "two" after 600 throws would therefore be close to 100.
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