Probability Calculator

Work out the probability of A and B, A or B, not A, exactly one, neither, and conditional probabilities for two events, plus the chance of something happening at least once in repeated tries.

Two events, A and B

Probability results
EventProbabilityRule
P(A and B)0.1500P(A) × P(B) = 0.5 × 0.3
P(A or B)0.6500P(A) + P(B) − P(A and B) = 0.5 + 0.3 − 0.15
P(not A)0.50001 − 0.5
P(not B)0.70001 − 0.3
P(A xor B) — exactly one0.5000P(A or B) − P(A and B)
P(neither)0.35001 − P(A or B)
P(A | B)0.5000P(A and B) ÷ P(B) = 0.15 ÷ 0.3
P(B | A)0.3000P(A and B) ÷ P(A) = 0.15 ÷ 0.5
AB

Repeated independent tries

At least once
0.6723
Every time
0.0003
Never
0.3277

At least once = 1 − (1 − 0.2)^5 = 1 − 0.3277 = 0.6723

Formula P(A or B) = P(A) + P(B) − P(A and B) P(A | B) = P(A and B) ÷ P(B)

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The rules

  • Complement: P(not A) = 1 − P(A).
  • Multiplication, independent events: P(A and B) = P(A) × P(B).
  • Addition: P(A or B) = P(A) + P(B) − P(A and B). The subtraction stops the overlap being counted twice; for mutually exclusive events it is 0.
  • Conditional: P(A | B) = P(A and B) ÷ P(B), the probability of A once you know B happened.

Independent vs mutually exclusive

These are often confused. Independent means one event doesn’t change the other’s probability (two coin flips). Mutually exclusive means they can’t both happen (rolling a 2 and a 5 on one die). Mutually exclusive events with non-zero probabilities are never independent: knowing one happened tells you the other didn’t.

Frequently asked questions

How do I calculate “at least once”?

Use the complement: P(at least once in n tries) = 1 − (1 − p)ⁿ. The chance of at least one six in four rolls is 1 − (5/6)⁴ ≈ 0.518.

Can I enter percentages?

Enter probabilities as decimals between 0 and 1: 30% is 0.3.