Birthday Paradox

This lecture explores the concept of the birthday paradox, discussing the probability of two people sharing the same birthday in a group. Starting with a scenario of 25 students in a math class, the instructor explains the theoretical assumptions and calculations involved in estimating the likelihood of a shared birthday. Through the analysis of different inequalities, logarithmic functions, and exponential transformations, the lecture provides a detailed proof of the proposition. The final result reveals that the probability of a shared birthday among 25 students falls between 55.94% and 58.40%, with a more precise estimation of around 56.77%.