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Probability Calculator

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  • Gacha Complete-Collection Expected Number of Draws Calculator
    Gacha Complete-Collection Expected Number of Draws Calculator
    Calculate the expected number of gacha pulls or capsule-toy draws to collect every item in a set, using the Coupon Collector formula E(n)=n*H(n).
    June 18, 2026
  • Hybrid Lognormal Distribution (PDF / CDF) Calculator
    Hybrid Lognormal Distribution (PDF / CDF) Calculator
    Compute the hybrid lognormal distribution HybLogN(rho x, mu, sigma): density f(x), lower cumulative P(x) and upper cumulative Q(x), tabulated over a range.
    June 18, 2026
  • One-Sample Z-Test for Significance
    One-Sample Z-Test for Significance
    Test whether a sample mean differs significantly from a known population mean. Computes the z statistic, critical z, p-value, and reports significance.
    June 18, 2026
  • Inverse Chi-Square Distribution Percent Point Calculator
    Inverse Chi-Square Distribution Percent Point Calculator
    Find the chi-square distribution quantile (percentage point) from a lower- or upper-tail probability and degrees of freedom by inverting the CDF. Free online tool.
    June 18, 2026
  • Inverse Chi-Squared Distribution Calculator
    Inverse Chi-Squared Distribution Calculator
    Compute the PDF, lower and upper cumulative probability of the inverse chi-squared distribution for any point x and degrees of freedom nu.
    June 18, 2026
  • Stirling Numbers of the Second Kind Table Calculator
    Stirling Numbers of the Second Kind Table Calculator
    Compute an exact table of Stirling numbers of the second kind S(n,k) for k = 0..n, with arbitrary-precision integers and the Bell number row sum.
    June 18, 2026
  • Stirling Numbers of the First Kind (Table)
    Stirling Numbers of the First Kind (Table)
    Compute the full row of signed Stirling numbers of the first kind s(n,k) for k = 0..n. Enter n and get a clean table plus signed and absolute sums.
    June 18, 2026
  • Stirling Numbers of the Second Kind S(n,k) Calculator
    Stirling Numbers of the Second Kind S(n,k) Calculator
    Compute the Stirling number of the second kind S(n,k): the number of ways to partition n labeled elements into k non-empty unlabeled subsets.
    June 18, 2026
  • Stirling Number of the First Kind Calculator
    Stirling Number of the First Kind Calculator
    Compute the signed Stirling number of the first kind s(n,k) for non-negative integers n and k, the falling-factorial coefficients, with a worked example.
    June 18, 2026
  • Subset Calculator
    Subset Calculator
    Count the total number of subsets of an n-element set (2ⁿ) and the number of subsets of size k using the combination formula C(n,k).
    June 18, 2026
  • Probability Someone Shares Your Birthday Calculator
    Probability Someone Shares Your Birthday Calculator
    Find the chance that at least one other person in a group shares YOUR exact birthday using p = 1 - (364/365)^(n-1). The "matches mine" birthday problem.
    June 18, 2026
  • IQ Percentile Calculator
    IQ Percentile Calculator
    Convert any IQ score to its percentile rank using the normal distribution. Supports SD 15, 16 and 24 scales with the standard normal CDF.
    June 18, 2026
  • Permutations with Repetition Table Calculator
    Permutations with Repetition Table Calculator
    Build a table of permutations with repetition nΠr = n^r for a fixed set size n while r ranges from a start to an end value, with big-integer precision.
    June 18, 2026
  • Incomplete Beta Function & Regularized Incomplete Beta Function Table Calculator
    Incomplete Beta Function & Regularized Incomplete Beta Function Table Calculator
    Build a table of the lower incomplete beta function Bx(a,b) and the regularized incomplete beta Ix(a,b) over a range of x for given shape parameters a and b.
    June 18, 2026
  • Combinations nCr Table Calculator
    Combinations nCr Table Calculator
    Tabulate the binomial coefficients nCr for every r from 0 to n. Computes combinations with exact big-number arithmetic and the 2^n row sum, n up to 300.
    June 18, 2026
  • Permutations nPr Table Calculator
    Permutations nPr Table Calculator
    Generate a full table of permutations nPr for r = 0 to n using nPr = n!/(n-r)!. Exact big-integer results for ordered arrangements of distinct objects.
    June 18, 2026
  • Combinations with Repetition Table Calculator
    Combinations with Repetition Table Calculator
    Compute a table of combinations with repetition H(n, r) = C(n+r-1, r) for n distinct items, with r ranging over any integer interval. Exact big-integer results.
    June 18, 2026
  • Poisson Lambda from Cumulative Probability Calculator
    Poisson Lambda from Cumulative Probability Calculator
    Solve for the Poisson mean lambda from a known cumulative probability and percentile point x. Supports lower P(X less or equal x) and upper Q(X greater or equal x) modes.
    June 18, 2026
  • Punnett Square Calculator
    Punnett Square Calculator
    Free Punnett square calculator for a monohybrid cross. Enter both parents' alleles to get offspring genotype and phenotype ratios and probabilities.
    June 18, 2026
  • Rock-Paper-Scissors Decisive Round Probability Calculator
    Rock-Paper-Scissors Decisive Round Probability Calculator
    Compute the probability a rock-paper-scissors (janken) game with n players is decided within r rounds, and rounds needed for a 99% chance of a decision.
    June 18, 2026
  • Incomplete Beta Function Calculator
    Incomplete Beta Function Calculator
    Compute the lower incomplete beta function B_x(a,b) by numerically integrating t^(a-1)(1-t)^(b-1) with Gauss-Legendre quadrature. Set x=1 for the complete beta function.
    June 18, 2026
  • Combination with Replacement Calculator
    Combination with Replacement Calculator
    Calculate combinations with replacement (multisets) using C(n+r-1, r). Enter the number of item types and items chosen to get the count instantly.
    June 18, 2026
  • Permutation and Combination Calculator
    Permutation and Combination Calculator
    Free permutation and combination calculator. Compute P(n,r) ordered arrangements and C(n,r) selections from n items instantly with formulas and examples.
    June 18, 2026
  • Mean, Median, Mode, Range Calculator
    Mean, Median, Mode, Range Calculator
    Calculate the mean, median, mode, range, sum, min and max of any data set. Free online statistics calculator — just paste your numbers.
    June 18, 2026
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