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Hello everyone! I hope that you are all doing well during this crazy time. I have finally completed my MAT 380 seminar on The Birthday Paradox and Monty Hall Problem. It wasn’t easy, and I really struggled with LaTeX at first, but I think things really came together at the end. I really appreciate any advice, feedback, or tips that you have to offer. I also wanted to include a quick note before my abstract to thank all of those who were so kind as to help explain to me what seminars were all about, and assure me that my presentation topic was a good choice. I really appreciate it! Good luck to everyone with final exams approaching, and good luck to the seniors who are sadly leaving us!

### Abstract:

The study of probability is one of the most useful applications of math in the world around us. Yet, when we apply basic probability rules to real-world examples, the results can be pretty surprising and seem rather unlikely. Our expectations or perceptions of what goes on in the world around us may lead us to draw false conclusions about the likelihood of an event.

This is the case for both the Birthday Paradox and Monty Hall Problem (hence the words paradox and problem in their names). The Birthday Paradox demonstrates that the number of people you need in a room to have a 50% chance that two people share a birthday is much lower than most people would expect. The Monty Hall Problem is based off of the final round of the popular game show Let’s Make a Deal. This problem continues to stump mathematicians around the world, and is still disputed by some today. As my presentation will show, this problem boils down to a conditional probability problem, and recognizing this could actually increase the contestant’s odds of winning. My presentation
will demonstrate how these two problems can be easily solved with probability rules, despite their relatively surprising results when interpreted contextually.