MONTE CARLO

ACTIVITY-2: Perform a Monte Carlo Simulation using Google Colab.

The Birthday Paradox, also known as the Birthday Problem, is a fascinating demonstration of the counterintuitive nature of probability. It reveals that in a surprisingly small group of people, the probability of two individuals sharing the same birthday is much higher than commonly perceived. In this Monte Carlo simulation, we aim to delve into this intriguing phenomenon by utilizing the Monte Carlo method to simulate and analyze the likelihood of shared birthdays within a group of individuals. Through this simulation, we seek to gain a deeper understanding of the underlying probabilistic concepts and demonstrate the practical application of Monte Carlo techniques in exploring real-world scenarios. 

I conducted a Monte Carlo simulation to explore the Birthday Paradox, which is a probability puzzle that reveals the unexpected likelihood of shared birthdays within a small group of people. By leveraging the Monte Carlo method, I was able to simulate and analyze the probability of individuals within a group sharing the same birthday. This approach allowed me to gain insight into the counterintuitive nature of the Birthday Paradox and its implications. 

GOOGLE COLLAB LINK:  birthday_paradox.ipynb - Colab (google.com) 

Screenshot of the Code and the Manual Calculation Performed

Comparison of Coding Approach and Manual Calculation

In exploring the Birthday Paradox, we employed both a computational Monte Carlo simulation and a practical, hands-on approach, providing a comprehensive understanding of this counterintuitive probability phenomenon. Our coding approach involved implementing a Python script to simulate 10,000 trials, each with a group of 23 people. The program randomly assigned birthdays and efficiently tallied the occurrences of shared birthdays across all trials. This large-scale simulation yielded results closely aligning with the theoretical probability of approximately 50.73%. In contrast, our practical approach involved physically enacting several small-scale trials. We gathered groups of 23 volunteers, recorded their actual birthdays, and checked for matches. While this method provided a tangible, real-world demonstration of the paradox, it was limited in scale compared to the computational method. The coding approach allowed for rapid execution of a vast number of trials, providing statistically robust results, while the practical approach offered an intuitive, hands-on experience that made the concept more relatable and memorable. Together, these methods complemented each other, with the computational simulation validating the theoretical probability at scale, and the practical trials bringing the paradox to life in a way that resonated on a personal level. This dual approach not only confirmed the surprising frequency of birthday matches in small groups but also illustrated the power of combining theoretical calculations with both virtual and real-world experimentation in understanding complex probabilistic concepts.