Probability

How to use this category

Probability pages give a distribution a specific convention and then stick to it. Geometric waits for the first success and counts that trial. Negative binomial counts failures before a set number of successes. Exponential uses a rate. Bayes is taught with a natural frequency tree because a lone percentage is easy to misread. Factorials, permutations, combinations, and modulo are here because they are counting tools, not disguised summaries of a sample.

Name the convention before you trust the probability. A geometric question that counts failures only will not match a page that counts the trial of the first success. A negative binomial that counts trials until r successes will not match a page that counts failures before those successes. The steps state which one we use. Bayes is here because a screening question is a probability question that people misread as a test of the person rather than a test of the information. The natural frequency tree per 10,000 people is the point of that page. Factorials, permutations, and combinations are exact integer tools. Modulo is here because remainder arithmetic is not a statistics summary and does not become one by sitting near a mean.

The cards above are the whole category, with one sentence on the job each page actually does. Open a page when that sentence matches the decision in front of you. If the sentence is close but the assumption is wrong, read the comparison section on the page before you copy a number into a report, a bid, or a lesson plan.

Worked examples are prefilled so the first result is auditable. Change one input and the ticket updates. The essay under the ticket walks the same arithmetic in sentences, then a second example, then the move that most often breaks the definition. Five questions at the end answer the objections a careful reader raises after seeing the figure. That structure is repeated because the habit of checking is the point, not because the formulas are the same.

Internal links leave this category only when the next formula genuinely lives next door. A standard deviation page may point at variance and at a t test. It should not point at a decking calculator. If you arrived from search on a broad word, use the one-sentence descriptions to discard the near misses. Near misses are how people report a p-value from a test they did not run.

Each worksheet in Probability keeps one H1, a canonical URL that matches the tool name, and meta text sized for search snippets. The steps are part of the page, not a hidden modal. If you teach from these pages, project the ticket and the assumptions together so students see the same definition you graded against.

When two tools in Probability look alike, read the blurb under each name before you commit. The difference is usually a divisor, a critical value, a waste percent, or a caution that belongs on one page and not the other. That difference is why the URLs stay separate.

Reviewed 21-10-2026. Pages in Probability currently include Bayes Theorem Calculator, Binomial Distribution Calculator, Combination Calculator, Conditional Probability Calculator, Empirical Rule Calculator, Expected Value Calculator, Exponential Distribution Calculator, Factorial Calculator, Geometric Distribution Calculator, Hypergeometric Distribution Calculator, Inverse Normal Distribution Calculator, Modulo Calculator, Negative Binomial Distribution Calculator, Normal Approximation to Binomial Calculator, Normal Distribution Calculator, Percentile to Z-Score Calculator, Permutation Calculator, Poisson Distribution Calculator, Probability Calculator, Raw Score Calculator, Uniform Distribution Calculator, Z-Score Probability Calculator, Z-Score to Percentile Calculator.

Every probability page

• Bayes Theorem Calculator Turns prevalence, sensitivity, and specificity into positive and negative predictive values and a count tree per 10,000 people.
• Binomial Distribution Calculator Gives the binomial point probability, both cumulative tails around k, and the mean and variance np(1 − p).
• Combination Calculator Computes the exact integer nCr and, for a small n, shows the multiply-and-divide build.
• Conditional Probability Calculator Divides a joint probability by P(B) and, when P(A) is present, checks whether independence approximately holds.
• Empirical Rule Calculator Applies the 68-95-99.7 rule to a mean and standard deviation for a roughly normal set.
• Expected Value Calculator Sums value times probability, reports the variance, and warns when the probabilities miss 1 by more than 0.02.
• Exponential Distribution Calculator Uses the rate parameterization: density lambda e^(−lambda x), cdf 1 − e^(−lambda x), and mean 1/lambda.
• Factorial Calculator Returns an exact integer factorial from 0 through 1000, or the gamma extension for a non-integer from 0 to 170.
• Geometric Distribution Calculator Uses the trials-until-first-success convention: P(X = k) = (1 − p)^(k − 1) × p, with mean 1/p.
• Hypergeometric Distribution Calculator Gives the probability of k successes in a draw without replacement, plus the mean nK/N.
• Inverse Normal Distribution Calculator Turns a tail probability, a mean, and a standard deviation into the raw score that cuts off that tail.
• Modulo Calculator Shows the JavaScript truncated remainder, the floor remainder, and both quotients. Rejects a divisor of 0.
• Negative Binomial Distribution Calculator Counts failures before the r-th success: C(k + r − 1, k) × p^r × (1 − p)^k, with mean r(1 − p)/p.
• Normal Approximation to Binomial Calculator Places a continuity-corrected normal probability for P(X ≤ k) beside the exact binomial cdf when n is at most 200.
• Normal Distribution Calculator Turns a raw score, a mean, and a standard deviation into a z-score, a density, and both tail probabilities.
• Percentile to Z-Score Calculator Converts a percentile or cumulative probability into the matching standard normal z.
• Permutation Calculator Computes the exact integer nPr = n! / (n − r)! as a falling product of r factors.
• Poisson Distribution Calculator Evaluates the Poisson probability of a count and the cumulative probability, with mean and variance both equal to lambda.
• Probability Calculator Applies one rule: the complement of p, the union of two events, or at least one success in n independent trials.
• Raw Score Calculator Rebuilds a raw score from a z-score, percentile, or tail probability plus a mean and sigma.
• Uniform Distribution Calculator Evaluates a continuous uniform density and cdf on the interval from a to b, plus the mean and variance.
• Z-Score Probability Calculator Returns the standard-normal probability to the left of z, to the right of z, or between two z values.
• Z-Score to Percentile Calculator Reports the left-tail percentile of a standard normal z-score.