Probability Calculator

Enter probabilities as percentages (30 for 30%) and pick the rule that matches your assumption: independence, mutually exclusive, or a known overlap.

How it works

Independence means P(A and B) = P(A)P(B). Mutually exclusive events cannot both happen, so P(A or B) = P(A)+P(B) and that sum cannot exceed 100%. When they can overlap, subtract P(A and B). The complement is 1 − P(A).

“At least once” in n independent trials is 1 − (1 − P(A))ⁿ. Inputs outside 0–100% are rejected.

Formula

P(A and B) = P(A)P(B)   (independent)
P(A or B) = P(A) + P(B)   (exclusive)
P(A or B) = P(A) + P(B) − P(A and B)
P(not A) = 1 − P(A)
P(at least one) = 1 − (1 − P(A))ⁿ

Worked examples

Independent and
30% and 40% → 12%
Complement
P(A) = 25% → P(not A) = 75%

Useful notes

This is not a Bayes calculator and does not update from a test result.

FAQ

When can I multiply probabilities?: When the events are independent — knowing one happened does not change the other.
When can I add them?: When they cannot happen together (mutually exclusive). Otherwise subtract the overlap.
Why do I enter 30 instead of 0.3?: These fields are percentages. 30 means 30%.

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