MATH201 - W5 - What are the chances Assignment Template

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Bryant & Stratton College *

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Statistics

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Jan 9, 2024

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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? Theoretical probability refers to the likelihood of an event occurring based on mathematical calculations and reasoning. It is determined by dividing the number of favorable outcomes by the total number of possible outcomes. For example, when flipping a fair coin, the theoretical probability of getting heads is 1/2. On the other hand, experimental probability is based on actual observations and data collected from conducting experiments or surveys. It involves performing repeated trials to determine the frequency of an event occurring. For instance, if we flip a coin 100 times and get heads 60 times, then the experimental probability of getting heads would be 60/100 or 0.6. When it comes to reliability, theoretical probability is considered more reliable because it is based on logical calculations and assumes that all outcomes are equally likely. However, its accuracy depends on the assumptions made about the system under consideration. Experimental probability can be affected by various factors such as sample size, bias in data collection, or limited observations. Nevertheless, experimental probability provides real-world evidence which may be valuable in cases where theoretical predictions cannot account for all variables accurately. Therefore, both types of probabilities have their significance depending on the context and purpose they are used for. 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). There is only one way to roll a two with one standard die, and the die has six equally likely outcomes. Therefore, the theoretical probability of rolling a two is 1/6. As a decimal, this probability is equal to 0.167 (rounded to three

decimal places). As a percentage, this probability is equal to 16.7% (rounded to one decimal place). 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). 3/25, 0.120, 12% Roll Number | Outcome 1 | 4 2 | 6 3 | 5 4 | 2 5 | 1 6 | 3 7 | 2 8 | 6 9 | 4 10 | 5 11 | 1 12 | 3 13 | 6 14 | 4 15 | 2 16 | 1 17 | 5 18 | 2 19 | 3 20 | 6 21 | 4 22 | 5 23 | 1 24 | 3 25 | 5

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. In this case, our experimental probability is not equal to the theoretical probability. This can be due to random chance or variability in our trials. Rolling the die for only our age in years may not provide an accurate representation of the true probability. If we were to double the number of times we roll the die, it would likely result in a closer approximation to the theoretical probability. Increasing the sample size reduces random fluctuations and brings us closer to expected values based on theory. By doubling the number of rolls, we increase our chances of observing different outcomes and approaching the true probabilities associated with each outcome on a fair die. With a larger sample size, any discrepancies between experimental and theoretical probabilities are less likely and tend to diminish. However, it's important to note that even with a larger sample size, there will still be some degree of randomness involved. The law of large numbers tells us that as the sample size increases, experimental results will converge towards theoretical probabilities, but they may not be exactly equal. In summary, doubling the number of rolls would likely result in a closer approximation to the theoretical probability because it reduces random fluctuations and brings us closer to expected values based on theory.

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