MATH201 - What are the chances Assignment- Felice White

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Bryant and Stratton College, Buffalo *

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201

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Statistics

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Jun 2, 2024

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docx

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Uploaded by DoctorWaterAlpaca37

Week 5 – Assignment 2 – What are the chances? - 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? The concept of probability involves predicting or recording the likelihood of certain events occurring. There are two main types of probability: theoretical probability and experimental probability. Theoretical probability is based on all possible outcomes and provides a prediction of what will happen. On the other hand, experimental probability is the result of actual observations or recordings of events that have occurred. In my opinion, experimental probability is more reliable because it is based on real data. Theoretical probability can be useful for making predictions, but it does not always reflect what happens in real life. Through the process of conducting experiments and gathering data, we can obtain a more comprehensive understanding of the probability and frequency of certain events occurring. This knowledge can be applied to make more informed decisions based on the insights gained, helping us to better assess the risks and opportunities associated with various scenarios. By analyzing the data collected, we can uncover patterns, trends, and potential correlations that may not be immediately apparent, allowing us to make more accurate predictions and develop effective strategies. Ultimately, the systematic approach of data collection and analysis can be a valuable tool in improving decision-making processes across a wide range of industries and applications. 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). 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). Age 38 (1,6,1,3,6,1,1,4,3,5,6,4,2,1,2,5,3,4,6,2,4,5,4,2,5,3,4,6,1,3,5,3,1,3,6,4,2,1) 1 4 7 10 13 16 19 22 25 28 31 34 37 0 1 2 3 4 5 6 7 A rolling die 38 times Fraction 1/38 Decimals 0.026 Percentage 2.6% 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. During the experimental probability experience, which I trust more than the theoretical probability concept, I conducted a study in which I rolled a six-sided die 38 times. Over the course of the experiment, I observed the number 2 appearing a total of 5 times. This data is

significant because it provides insight into the probability of rolling a 2 on the die, which can be useful in various statistical analyses. As stated, Theoretical probability is based on all possible outcomes and provides a prediction of what will happen. This result allowed me to calculate the experimental probability of getting a 2, which turned out to be 5/38. Interestingly, this value is equal to the theoretical probability of getting a 2, which is 1/6 Based on the results of my experiment, which involved rolling a die multiple times and recording the outcomes, it can be inferred that the theoretical probability of rolling a 2 on a die is accurate. The data collected during the experiment aligns with the expected probability, indicating that the die is fair. Therefore, we can conclude that the die has an equal chance of landing on any of its six sides, as expected from a fair die.

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