Probability Calculator
Compute probabilities of single events, joint events, and complements using basic probability rules.
Probability, sampling, and descriptive statistics made readable.
Means, medians, standard deviations, confidence intervals, and sample size planning — with formulas and worked examples for each tool.
Compute probabilities of single events, joint events, and complements using basic probability rules.
Convert a raw value into a z-score using the mean and standard deviation of its distribution, and look up the correspond...
Compute the posterior probability P(A|B) from the prior P(A), the likelihood P(B|A), and the false-positive rate P(B|¬A)...
Count how many ways to choose or arrange r items from a set of n — both nPr and nCr, with a short breakdown of why they...
Convert a standard-normal z-score into the corresponding cumulative percentile (Φ(z)) using a high-accuracy logistic app...
Work out how many respondents you need for a given confidence level, margin of error, and population size.
Compute the odds of winning a "pick k from n" lottery (e.g. 6/49) — the probability of matching all k drawn numbers, exp...
Compute the expected value and variance of rolling N identical fair dice (each with S sides), using E = N · (S+1)/2 and...
Compute pot odds (the ratio of the call amount to the total pot after the call), the required equity to make a profitabl...
Calculates the exact binomial probability P(X = k) = C(n,k) · pᵏ · (1−p)^(n−k), the mean μ = n·p, and standard deviation...
For Catan and other 2d6 games, compute the probability that at least one of your favoured numbers will come up over K ro...
Compute the expected value of a discrete random variable defined by up to five (probability, payoff) pairs. Reports E[X]...
Compute P(X = k), the probability that the first success in a Bernoulli sequence occurs on trial k, using the shifted ge...
Compute the binomial coefficient "n choose k" using factorials. Useful for combinations, Pascal's triangle, and binomial...
Compute the probability density function of a normal distribution N(μ, σ²) at a given value x, using f(x) = exp(−(x − μ)...
Compute the probability density function f(t) = λ · e^(−λt) and the survival function S(t) = e^(−λt) of an exponential d...
Compute the χ² goodness-of-fit test statistic for up to four categories, given the observed counts and the expected coun...
Calculates Poisson probabilities: P(X=k) = e^(−λ)·λᵏ/k!, and the cumulative P(X≤k) by summing from 0 to k. Used for coun...
Calculates the minimum detectable effect MDE = (z_α + z_β) × √(2σ²/n), where z_α is the critical value and z_β correspon...
Calculates the sample size per variant needed for an A/B test: n ≈ 2 × [z_α/2 + z_β]² × p̄(1−p̄) / (p₁−p₂)², using the p...
Calculates the multinomial coefficient n!/(n₁!·n₂!·n₃!) and the probability of each outcome when items are drawn from a...
Updates a Beta(α, β) prior with n trials and k successes to get the posterior Beta(α+k, β+n−k). Returns posterior mean,...
Calculates χ² = Σ(O−E)²/E from observed and expected frequencies in up to a 4-cell (2×2) contingency table, and indicate...
Calculates the expected value E[X] = Σ xᵢ·P(xᵢ) and variance Var[X] = Σ(xᵢ−μ)²·P(xᵢ) for a discrete probability distribu...