Everyday is a Birthday A Journey to a classic problem through Math and Rust
This article explores the classic probability problem of ensuring every day of the year is represented by a birthday in a group of people, using mathematical concepts like the Coupon Collector Problem and Inclusion-Exclusion Principle. It calculates needing around 2364 students, adjusting to 2669 with leap days, and discusses the gamma function for probability calculation.
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This article delves into a classic probability problem regarding whether every day of the year is represented by a birthday in a group of people, specifically at Rice University. The author explores this question using mathematical concepts like the Coupon Collector Problem and the Inclusion-Exclusion Principle. By abstracting the problem and applying probability theory, the author calculates that approximately 2364 students would be needed to ensure all birthdays are covered. Additionally, the analysis extends to account for leap days, adjusting the number of students required to around 2669. The article also discusses the use of the gamma function to calculate the probability of seeing all birthdays in a group of students. Furthermore, the Inclusion-Exclusion Principle is introduced as a powerful combinatorial tool to calculate the probability of every birthday being represented in a group. Overall, the author provides a detailed and rigorous exploration of this intriguing probability problem, showcasing various mathematical techniques and approaches to tackle it.
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