Statistics
confidence interval calculator
Find the confidence interval around your estimate.
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Statistics calculators for conditional probability, Bayesian updating, classification metrics, one-way ANOVA, combinations, expected values and probability puzzles. Choose a calculator for an exact model result, or a coin/dice simulator for a random observation. Each tool states its sampling assumptions, input limits and undefined cases. Worked guides distinguish head counts from streaks, probability bounds from distribution estimates, and raw implied probabilities from normalized market shares. Existing confidence-interval tools remain available for their separate estimation questions. Additional Statistics tools cover joint and three-event probability, permutations, lottery counting, Monty Hall and Parrondo models, sample proportions, likelihood-ratio updates and risk comparisons. Two practice quizzes separate worked exercises from general calculators. Every model states its sampling rules; simulations remain distinct from calculated probabilities.
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Accuracy Calculator
Binary Accuracy Calculator: correct predictions, balanced accuracy, sensitivity and specificity from TP, FP, FN and TN.
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ANOVA Calculator
Run a classical one-way ANOVA from raw independent groups. Get the ANOVA table, F statistic, upper-tail p-value and eta squared.
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Bayes' Theorem Calculator
Update a prior probability using evidence likelihoods. Calculate posterior probability, total evidence probability and the likelihood ratio.
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Bertrand's Box Paradox
Solve Bertrand’s coin-box paradox with adjustable box priors and a uniformly observed gold or silver coin.
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Bertrand's Paradox
Compare random-chord probabilities under uniform endpoints, uniform center distance and disk-area midpoint sampling.
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Birthday Paradox Calculator
Calculate any-pair birthday collision probability and the minimum group size for a target, with adjustable uniform bucket count.
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Boy or Girl Paradox
Compare two-child conditional probabilities across at-least-one, older-child, random-child and independent-tag observation protocols.
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Chebyshev's Theorem Calculator
Find Chebyshev’s distribution-free coverage bound or the interval width required for a target, using a population mean and standard deviation.
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Coin Flipper
Flip a virtual coin with adjustable heads probability. Generate independent samples, heads/tails counts and a readable sequence preview.
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Coin Flip Probability Calculator
Calculate exact, at-least or at-most heads probabilities for independent fixed-probability coin flips using the binomial model.
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Coin Toss Streak Calculator
Calculate the probability of at least one head-only or either-side streak in a fixed number of flips, accounting for overlapping runs.
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Combination Calculator
Count unordered selections exactly with or without repetition. Use integer combinations for subsets and multisets without factorial overflow.
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Conditional Probability Calculator
Calculate both conditional directions from event marginals and a joint probability, with feasible-table checks and undefined-case handling.
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Confusion Matrix Calculator
Build a labeled binary confusion-matrix report with precision, recall, specificity, F1, balanced accuracy and Matthews correlation coefficient.
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Dice Average Calculator
Find expected total, variance, standard deviation and range for mixed fair-dice expressions with fixed integer modifiers.
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Dice Probability Calculator
Calculate fair-dice sum and chosen-face event probabilities with convolution or binomial counting, including exact and cumulative events.
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Dice Roller Calculator
Roll independent fair virtual dice in batches using unbiased integer sampling. View totals and compare observed and theoretical averages.
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Expected Value Calculator
Calculate a finite discrete expected value, variance and standard deviation from net outcomes and a complete probability table.
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False Positive Paradox Calculator
Explain base-rate effects with posterior precision and expected natural-frequency counts from prevalence, sensitivity and specificity.
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Implied Probability Calculator
Convert decimal, fractional and American odds to raw implied probabilities; optionally calculate complete-market overround and proportional shares.
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Joint Probability Calculator
Find an intersection probability from a marginal and conditional rate, an explicit independence assumption, or a joint count.
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Lottery Calculator
Calculate exact-match probabilities for one unordered lottery ticket, with an optional separate independent bonus pool.
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Monty Hall Problem Calculator
Compare staying and uniform switching under an informed-host Monty Hall protocol, with optional aggregate simulation.
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Odds Calculator
Convert success/failure weights into event odds and probability, then compare all-success and at-least-one independent repetition events.
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Parrondo's Paradox Calculator
Compare standalone and randomly mixed capital-dependent Parrondo games using finite-state expectations and stationary drift.
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Password Combination Calculator
Count policy-valid ordered character strings across a length range, with optional required disjoint character groups.
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Permutation Calculator
Count ordered distinct selections, repeated strings and fixed-multiplicity arrangements with exact integer arithmetic.
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P-Hat Calculator
Calculate an unweighted sample proportion and its plug-in binomial standard error from observed success and trial counts.
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Post-Test Probability Calculator
Update pre-test probability after a positive or negative result using test rates or a known likelihood ratio for that result.
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Probability Calculator
Calculate both, inclusive OR, exactly one and neither for two events under an explicit relationship model.
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Probability of 3 Events Calculator
Validate and calculate three-event probabilities from mutual independence or a full set of pairwise and triple intersections.
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Quiz: Dice Average Calculator
Practice six fair-dice mean and variance questions with numerical answer checks, explanations and session scoring.
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Quiz: Lottery Calculator
Practice six small lottery-counting questions with worked feedback and clearly labeled integer or decimal-probability answers.
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Random Number Generator
Generate uniform integers within inclusive bounds, allowing repeats or sampling without replacement using browser randomness.
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Relative Risk Calculator
Compare two observed group risks with a risk ratio, risk difference and supported approximate 95% log interval.
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Risk Calculator
Calculate expected loss from a hypothetical event probability and loss magnitude, while keeping consequence and spread separate.
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Roulette Payout Calculator
Check standard hypothetical roulette net profit, gross winning return, event probability and expected net result for two wheel sizes.
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Sensitivity and Specificity Calculator
Estimate sensitivity, specificity and positive/negative likelihood ratios from labeled validation counts without inventing undefined rates.
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Two Envelopes Paradox Calculator
Compare unopened-envelope expectations and observed-amount updates under an explicit finite prior for the smaller amount.
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