The Birthday Problem is one of those problem in probability that seem counter-intuitive at first glance but it is backed by elegant mathematical reasoning that proves it otherwise. It demonstrates the fact that in a group of just 23 people, there's a 50% chance of at least two individuals sharing a birthday, which feels very strange. From my observation, people frequently participate in groups or gatherings of 23 or more throughout their lives, yet they rarely come across instances of shared birthdays. Intrigued by this, i decided to create a script to visualize and better understand it.

The script below takes number of trials N and on each trial it generates 23 persons and assign them random birthdays. Using this data, it produces a graph that shows the cumulative probability across all trials and remarkably it converges to 50%.

It also creates a heatmap to provide further insights where rows represent trials and columns represent days of the year. The color coding is green pixel for no birthdays, yellow pixel for single birthdays, and red pixel for shared birthdays.