Probability Calculator
Basic probability, complements, combinations (nCr), permutations (nPr), and union/intersection of independent events.
How to use
- 1
Pick the calculation you need (single event, complement, nCr, nPr, union, intersection).
- 2
Fill in the inputs that appear for that mode.
- 3
Probabilities can be entered as decimals between 0 and 1 (e.g. 0.25 = 25%).
Frequently asked questions
Combinations (nCr) count selections where order doesn't matter — picking 3 students from 10 for a group photo. Permutations (nPr) count arrangements where order matters — picking 3 students for gold, silver, bronze medals. nPr is always larger than or equal to nCr.
Two events are independent if one happening doesn't affect the probability of the other. Coin flips and dice rolls are independent. Drawing cards without replacement is NOT independent. The union/intersection formulas here assume independence.
P(A or B) = P(A) + P(B) − P(A) × P(B). The subtraction prevents double-counting the overlap. For mutually exclusive events (can't happen together), the formula simplifies to P(A) + P(B).
JavaScript's Number type overflows around 170! (≈ 7.3 × 10³⁰⁶). For factorials and combinations involving larger n, the calculator would return Infinity, which is useless. If you need bigger values, use a symbolic math system.
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Source: Standard probability formulas · Last verified 2026-06. This tool provides estimates only and is not legal, tax or financial advice. Always verify your specific situation with the relevant UAE authority or a licensed advisor before taking action.