Probability Practice vs Probability Paradox Lab

Probability Practice is an educational application designed to help students understand and practice probability concepts through structured quizzes and mock tests. The app provides topic-wise questions covering fundamental and advanced probability topics commonly studied in mathematics and statistics courses. Students can practice conceptual questions, solve numerical problems, and monitor their performance using statistics. The app supports independent learning and systematic revision of probability concepts. Topics Included 1. Basic Concepts of Probability Random experiments, sample space, events, simple and compound events, and equally likely outcomes. 2. Types of Events Mutually exclusive events, exhaustive events, complementary events, independent and dependent events, and equally probable events. 3. Classical Probability Classical probability definition, probability value range, certain and impossible events, complement rule, and basic probability problems. 4. Addition Theorem of Probability Addition rule, mutually exclusive events, general addition theorem, union and intersection of events, and related problems. 5. Conditional Probability Definition of conditional probability, conditional probability formula, dependent and independent events, multiplication rule, and problem solving. 6. Bayes’ Theorem Concept of Bayes’ theorem, prior and posterior probabilities, likelihood, total probability rule, and applications. 7. Random Variables Definition of random variables, discrete and continuous random variables, probability distributions, probability mass functions, and probability density functions. 8. Mathematical Expectation Expected value, properties of expectation, variance, standard deviation, and expectation-related problems. 9. Probability Distributions Bernoulli trials, binomial distribution, mean and variance of binomial distribution, Poisson distribution, and distribution-based numerical problems. 10. Applications of Probability Applications in games, statistics, risk analysis, reliability analysis, decision theory, and real-life situations. Key Features Topic-wise probability practice quizzes Mock tests for overall assessment Daily quiz for regular practice Performance statistics to track progress Structured topics for systematic learning Simple and distraction-free interface Probability Practice is suitable for students studying probability in mathematics, statistics, and related fields who want structured practice and regular revision.

"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