Probability
Probability
Probability Report
The probability of an event can be determined in theory as well as in practice. In this project, you will use the formulas and methods in your readings to determine the theoretical probability. You will then conduct an experiment to see if the outcomes match what you expect to find with the theoretical probability.
In this project you will:
be able to calculate and interpret probability
be able to analyze and compare theoretical and experimental probabilities
To complete this project you will:
Complete the Probability Report Worksheet to guide you in writing your APA report. Be sure to show all work!
Complete a 2-page, double-spaced, APA-formatted report. In the report you need to present your findings and explain your conclusions on experimental and theoretical probability. Thoughts to include in the report include: How are theoretical and experimental probability different? Why might the theoretical probability not match the experimental probability?
Be sure to cite your sources for the questions that require sources.
Length/Formatting Instructions
Length 2 pages, 400-500 words
Font 12 point , Calibri Font, no more than 1″ margins
Program/File Type Submit in Word
Attachments Should be pasted into the Word document if possible.
Referencing system APA referencing system is necessary in assignments, especially material copied from the Internet.
For examples of correct citations, visit the following links:
http://owl.english.purdue.edu/owl/resource/560/01/
File Name
M7 Assignment: Probability Report Grading Rubric
Your work will be evaluated on the following criteria:
CATEGORY Exceeds Expectations Meets Expectations Does Not Meet Expectations Significantly Below Expectations
Presentation Style – Organization, Transitions, Tone (10 Points) 10 points
The assignment is presented with excellent organization, thoughtful transitions, and the appropriate tone. 8 points
The paper is adequately organized, but has some errors in the transitions or the tone. 4 points
The paper is poorly organized, or it contains ineffective transitions and/or inappropriate tone. 0 points
The paper displays little to no organization or transitions, and/or does not use the appropriate tone.
APA Format – Citations and References (5 Points) 5 points
All sources used for quotes and facts are credible and cited, and the references and in-text citations are all properly formatted. Each reference has an in-text citation and in-text citation has a reference. 4 points
All sources used for quotes and facts are credible and cited, but slight errors are present in the format of the in-text citations or references. Or there may be one in-text citation or reference missing. 2 points
Some sources used for quotes and facts are either not credible or there are significant errors in the in-text citations and/or references. Or there are multiple missing in-text citations or references. 0 points
The sources used for quotes and facts are not credible and/or not cited. The in-text citations and/or references are not present.
Application to the Real World (40 points) 40 points
The response indicates a high level application of probability. The paper demonstrates a complete understanding of the calculation of experimental probability. The paper addresses any inconsistencies with theoretical and experimental probability. 32 points
The response indicates a basic application of probability. The response demonstrates a clear understanding and analysis of experimental probability. The paper addresses any inconsistencies with theoretical and experimental probability. 16 points
The response indicates an incomplete application of probability. The response demonstrates a conceptual understanding and analysis of experimental probability. The paper addresses some inconsistencies with theoretical and experimental probability. 0 points
The response indicates little or no application and analysis of probability.
Accuracy (45 points) 45 Points
The entire assignment was completed with dedicated attention to the directions. Outstanding effort and work exceeds expectations. All work is shown and calculations are accurate. 36 Points
Most of the assignment was completed with attention to the directions but some parts are missing. Good effort and work meets expectations. Most calculations are accurate. 18 Points
Assignment was completed but attention to the directions was spotty or parts of the assignment are missing. Some effort was made and work meets minimal expectations. Only some calculations are accurate. 0 points
Assignment is incomplete and/or directions were not followed. Lacks many elements. Appears that little or no effort was made. Calculations are not accurate.
ANSWER
PROBABILITY REPORT WORKSHEET
Probability of obtaining heads on a coin toss
A coin has two sides. This implies that there are two possible outcomes, heads or not heads (tails). For a fair coin, there is equal chances of the coin landing on either sides when tossed. Putting into consideration that probability is the number of ways you can achieve the desired outcomes divided by the total number of outcomes, and that the desired outcome is heads, then the theoretical probability of getting heads is calculated as
The total probability is 1. The probability of not heads is thus the difference between 1 and probability heads.
The complete trial of tossing a coin 100 times is as recorded below.
| H T H H H T H T H T T H T T H T T T T H T H H H H T H H T H T T H T H T T H T T H H T H T T H H T H T T H T T H H H H T T H T T H T T H H H T H T T H T H T H T T H T H T H T T H T H T H H T H T H T T |
The chosen scenario is getting heads. The experiments yields 48 heads. The experimental probability for the chosen scenario is
The experiment yields 52 outcomes of not heads. Therefore, the probability not heads is
The theoretical probability does not match the experimental probability. The theoretical probability for the desired outcome is while the experimental probability is .
The probabilities do not match. This is because theoretical probability is the expected outcome while experimental probability is the result obtained from an experiment that has been conducted. Both the expected outcome and the experimental outcome yield different results and thus the difference in the probabilities (Theoretical & Experimental Probability, 2020).
Theoretically, by flipping the coin 1,000 times I would expected to get 500 heads and 500 tails since each half an equal chance of occurring. However, through carrying out the experiment the desired outcome may be different from 500 heads and thus yield less or more than 500 heads (Theoretical & Experimental Probability, 2020).
References
Theoretical & Experimental Probability. (2020).
