MicroLector vs Probability Paradox Lab

MicroLector: Your learning app. Create your own voice-enabled microlessons or browse through our vast collection. For students, teachers and instructors EXPERT-REVIEWED MICROLESSONS Cybersecurity US Citizenship Tests Algebra Course History Fun stuff such as country flags and much more TUTORS Stuck with a difficult problem? Ask a question or take a picture of it and we will deliver a full solution and explanation for several subjects. We're adding tutors weekly, so if your subject is not yet available check back soon. CREATE & SCAN Scan vocabulary lists for easy import Create your own microlesson on your iPhone or iPad to prepare for any exam. Create a list of favorite lessons Extensive statistics Share your created microlesson with anyone privately (Your microlesson can only be accessed with people who have the link) Share your results with colleagues, teachers, parents through the "Result sharing" option FOR TEACHERS/INSTRUCTORS Review your students progress via the "Share results" feature Set push reminders for students who have started but not finished the lesson FOR STUDENTS MicroLector offers you a wide array of microlessons to prepare for your exams or admission tests. All microlessons have been created by experts. VOICE PLAY Go through the question via voice command. The app reads the questions and you can answer only via voice: In the car, on the bike, while doing chores around the house etc. Please review our app and let us know what you enjoy and what we can improve! For suggestions, please write us to team@microlector.com Visit us at http://microlector.com Like us on Facebook: www.facebook.com/microlectorapp

"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 20 more paradoxes and Quiz Mode across all 24 themes (72 questions). 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. Survivorship Bias Bullet holes on bombers that came back mark where a plane can be hit and still fly home. Armor the untouched parts. Regression to the Mean Praise and they slip, scold and they improve — not the coaching, just probability swinging back. Gambler's Ruin Even on a perfectly fair coin, the side with the smaller bankroll goes broke almost every time. Buffon's Needle Drop needles on a lined floor and you can measure π. Pólya's Urn Return the color you drew plus one more, and early luck gets locked in forever. The Arcsine Law The fairer the contest, the more one side leads the whole way. A near-even split is the rarest outcome. Bertrand's Paradox "A random chord" has three answers — 1/3, 1/2 or 1/4 — depending on how you define random. The Sleeping Beauty Problem Halfers and thirders. Change what you count and both answers stand. [ PERFECT FOR ] - Math & statistics enthusiasts - Curious minds who love "why?" - Brain teaser & trivia fans - Students and lifelong learners