Birthday Paradox Simulation
Simulation
Parameters
Simulated Probability:0.00%
Theoretical Probability:0.00%
Simulation Chart
How to Interpret the Results
- The blue line shows the simulated probability as more trials are run
- The red dashed line shows the theoretical probability
- With 23 people, there's about a 50% chance of a shared birthday
- The simulation helps visualize how quickly this probability increases with group size
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Understanding the Birthday Paradox
Overview
The Birthday Paradox demonstrates how our intuition about probability can be misleading. It shows that in a relatively small group of people, the probability of two people sharing a birthday is surprisingly high.
Mathematical Foundation
The probability is calculated using the complement rule:
For n people:
Key probabilities:
- 23 people: ~50% chance
- 30 people: ~70% chance
- 50 people: ~97% chance
- 70 people: ~99.9% chance