How likely is it?
Probability measures how likely an event is, from 0 (impossible) to 1 (certain), or 0% to 100%. This calculator covers three common situations: a single event, two events A and B, and repeated trials that either succeed or fail (the binomial distribution).
For two events you can choose whether they are independent (one does not affect the other) or mutually exclusive (they cannot both happen), and you get the chance of both, either, only one and neither.
How it is calculated
P(event) = favourable outcomes ÷ total outcomes
Independent: P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) − P(A and B)
Binomial: P(k) = C(n, k) × p^k × (1 − p)^(n − k)
Worked example
P(A) = 40% and P(B) = 25%, independent
- Both
- 10%
- At least one
- 55%
- Neither
- 45%
- Exactly 3 heads in 10 fair coin flips
- 11.72%
Common mistakes
- Do not add probabilities of events that can overlap without subtracting the overlap.
- Past results do not change independent events: a coin has no memory.
- Probabilities of all possible outcomes add up to 100%.