Bayesian P vs Probability Practice

Calculate probability of outcomes of clinical trials, by interpreting reported p-values in the context of scientific expectations, using prior probabilities of outcomes and Bayesian thinking. · p-values are frequently misused and misinterpreted ( see American Statistical Association statement on p-values) · Bayesian inference aids interpretation of p-values with reference to prior knowledge of the probability of the experimental outcome · P-value Interpreter permits realistic interpretation of reported p-values from user entered pre-trial probabilities of clinical trial outcomes and p-values for single and sequential trials · "Learn more" buttons lead to explanations of prior probabilities, p-values and Bayesian probabilities employed in calculating the direct probability of the trial outcomes (e.g. null hypothesis being false), illustrated with examples

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.