"With 23 people in a class, what's the chance two share a birthday?"
The answer exceeds 50%. Were you surprised?
Probability Paradox Lab is an interactive app that lets you experience mathematical paradoxes through simulation — results that feel wrong, yet are mathematically proven.
[ HOW IT WORKS ]
1. Make your intuitive guess
2. Run the simulation and see the real result
3. Read the math explanation and understand why
Be surprised by the answer. Be surprised again by the explanation.
[ FREE THEMES ]
Birthday Problem (Free)
With just 23 people, the probability of a shared birthday exceeds 50%. Why?
Monty Hall Problem (Free)
After the host opens a losing door, switching wins 2/3 of the time. Mathematically proven — yet deeply counterintuitive.
Two Envelopes Problem (Free)
A seemingly valid argument says you should always switch envelopes. Where's the flaw?
Coupon Collector Problem (Free)
Collecting all 10 kinds takes about 29 pulls on average. Fast at first, then it stalls.
[ PREMIUM THEMES ]
One-time purchase unlocks 12 more paradoxes and Quiz Mode across all themes. No subscriptions, no ads for premium users.
Ellsberg Paradox
Why do people prefer known odds over unknown ones — even when the math says they're equal?
Boy or Girl Paradox
"One child is a boy." How does that single fact change the probability?
False Positive Paradox
A 99%-accurate test says positive for a disease 1% of people have. You're sick with only ~50% odds.
Gambler's Fallacy
Five heads in a row. Is tails due? Randomness is clumpier than it looks.
St. Petersburg Paradox
Expected value is infinite, yet you'd pay little to play. Why?
Nontransitive Dice (Efron-style)
A beats B, B beats C, C beats A. No die is the strongest.
Parrondo's Paradox
Two losing games, played in alternation, somehow become a winning strategy.
Simpson's Paradox
A treatment wins in every subgroup — yet loses overall. How?
Secretary Problem
Interview one at a time with no going back. The optimal strategy for catching the best.
Benford's Law
About 30% of naturally occurring numbers start with a 1. A curious statistical bias.
Friendship Paradox
Your friends have more friends than you — the network bias that makes it true.
100 Prisoners Problem
If even one fails, all are executed. Yet one strategy saves everyone about 31% of the time.
[ PERFECT FOR ]
- Math & statistics enthusiasts
- Curious minds who love "why?"
- Brain teaser & trivia fans
- Students and lifelong learners
Show more
