Birthday Paradox

Explore the surprising probability of shared birthdays in groups through simulation and analysis

Overview

The Birthday Paradox demonstrates one of the most counter-intuitive results in probability: in a group of just 23 people, there’s a greater than 50% chance that two people share the same birthday. This simulation lets you explore why our intuition fails and verify the mathematics through Monte Carlo experiments.

Tips

1. Start with the 23-person case: Run simulations with 23 people to verify the surprising 50.7% probability and see it happen in real-time.

2. Try the 100-door analogy: Increase the group size to 100 people to see the probability approach certainty (99.99997%), making the math more intuitive.

3. Run large simulations: Execute 10,000+ trials to watch the empirical probability converge to the theoretical value, demonstrating the Law of Large Numbers.

4. Focus on pairwise comparisons: Remember that 23 people create 253 possible pairs, helping explain why the probability is so much higher than intuition suggests.

5. Test your predictions: Before running a simulation, guess the probability for different group sizes, then check your intuition against the results.