Paradoxes And Fallacies And The Probability And Statistics Behind Them
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Probability and statistics form the basis for many of the decisions that we make on a daily basis. However, as often as we weigh the probability of certain events or consequences occurring, we just as often make mistakes in our logic. In this thesis, I examine popular paradoxes and fallacies and seek to explain the mathematical concepts behind them, with the goal of providing a wider audience with examples of common contradictions and mistakes in logic and how to resolve them. I began by exploring various well-known paradoxes and fallacies in an effort to discover trends in misguided judgment. I selected nine of these and then further examined how they came about and how experts over the decades have aimed to solve them. By researching the solutions, I found that there were overlapping mathematical concepts behind them. I delved into these primary mathematical concepts and discovered that there were three that stood out: basic and conditional probability, expected value theory, and regression to the mean. I then sought to explain these three concepts in a way that would provide readers with the tools to solve the paradoxes in this thesis, as well as similar paradoxes and/or fallacies that they might encounter in the future. Additionally, I discussed real world applications for each of these tools in an effort to demonstrate to the reader how they might incorporate these newly acquired tools into their lives. The thesis concludes by recommending that paradoxes and fallacies be included in a college curriculum, since increased knowledge of them can contribute to better decision-making.