Probability Calculator
Calculate basic probability, combinations (nCr), permutations (nPr), and complement probability. Instant results with formulas.
Basic Probability P = Favorable / Total
Probability Formulas
Basic Probability: P(event) = (favorable outcomes) / (total outcomes). Values range from 0 (impossible) to 1 (certain).
Complement: P(not A) = 1 − P(A).
Combinations C(n,r): Number of ways to choose r items from n where order doesn't matter. C(n,r) = n! / (r! × (n−r)!).
Permutations P(n,r): Number of ordered arrangements of r items from n. P(n,r) = n! / (n−r)!.
Independent events: P(A and B) = P(A) × P(B). P(at least one) = 1 − P(none) = 1 − (1−P(A)) × (1−P(B)).
Frequently Asked Questions
Probability measures the likelihood of an event. It ranges from 0 (impossible) to 1 (certain). P = favorable outcomes / total outcomes.
Combinations count selections where order does not matter (C(5,2) = 10 ways to pick 2 from 5). Permutations count arrangements where order matters (P(5,2) = 20 ordered pairs).
The complement of event A is "A does not occur". P(not A) = 1 − P(A). Example: if P(rain) = 0.3, then P(no rain) = 0.7.
Multiply the individual probabilities together. P(A and B) = P(A) × P(B). For "at least one", use P = 1 − P(none occur) = 1 − (1−P(A)) × (1−P(B)).
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