Probability Paradox Lab vs Math Says Yes

"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

Most statistics sound wrong at first. In a room of 23 people, the odds of a shared birthday are already even. On a game show with three doors, switching after the host opens one doubles your chance of winning. A poll of 1,000 strangers can read a whole country. Math Says Yes is a feed of facts like these, each one explained until the surprise turns into something obvious. Open the app and start scrolling. Every fact is short and sourced, built around a single idea from probability or data. Most come with a quick question that catches your gut before it shows the answer, plus a small chart or a slider you can play with to watch the number move. What's inside: - A scrolling feed of counterintuitive statistics, from the birthday paradox to why tiny samples lie - Quick-check questions tuned to the exact intuition people get wrong - A daily challenge of five questions, so you can find out whether you beat your own guessing - Search and topics for digging into probability, sampling, averages, or plain randomness - Saved facts and a "learned" marker to track what has actually stuck - A glossary that explains the jargon in one paragraph instead of one textbook It costs nothing to read and needs no signup to start. Sign in only if you want to sync saved facts and progress across devices or build a streak. Made for the people who liked statistics in theory but never quite trusted it, and for anyone who enjoys being pleasantly wrong about numbers. Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/