Probability Calculator

Calculate probability of single events, combined events (AND/OR), permutations, and combinations.

This calculator runs five genuinely different formulas behind one Result field, switched entirely by the Calculation Type dropdown, and which inputs actually matter changes completely depending on which mode is selected. In Single Event mode, the default, Result is just Probability A read straight through — Probability B, Total Items, Chosen Items, and Number of Trials are all present on the page but none of them are referenced anywhere in that branch of the formula, so moving any of them leaves Single Event's Result exactly unchanged. Switch to A AND B and Result becomes the product of both probabilities, assuming independence; switch to A OR B and it becomes their sum minus that same product, which is the inclusion-exclusion formula that avoids double-counting the overlap between the two events. Permutations and Combinations mode abandon probabilities altogether and instead compute n! / (n − r)! or n! / (r!(n − r)!) from Total Items and Chosen Items, which is why Result switches from a percentage-like figure to a plain count in those two modes — the Result field is reused for two conceptually different kinds of number depending on the mode. Separately from whichever mode is active, At Least Once in N Trials always uses the binomial formula 1 minus (1 minus Probability A) raised to the Number of Trials, regardless of what Calculation Type is selected, which means it can report a meaningful figure even while the mode above it is set to Permutations or Combinations and has nothing to do with probability at all.