Birthday Paradox
A Classic Counterintuitive Probability
📚 Introduction
🎂 Birthday Paradox
How many people needed for >50% chance of shared birthday?
Intuition says many - after all, there are 365 days. But the answer will surprise you...
23
people for >50% probability
50
people for ~97% probability
70
people for >99.9% probability
🤔 Why so counterintuitive?
We're not asking 'someone shares YOUR birthday', but 'ANY two share a birthday'. 23 people form 253 pairs - each could match!
💡 The Math
It's easier to calculate 'all different': First person any day (365/365), second avoids first (364/365), third avoids both (363/365)... These multiply and shrink fast.
🌍 Real Applications
- Cryptography: Hash collision attacks
- Databases: Primary key collision probability
- Random generation: Duplicate detection
⚙️ Adjust Group Size
People vs Probability curve (yellow line marks 23)
🎮 Interactive Simulation
Probability of shared birthday among 23 people
50.7%
More than 50% chance of a match!
🎂
Click to generate random birthdays
📊 Batch Verification
📊
点击按钮运行批量模拟
Verify theoretical probability with data