Probability Calculator

Single-event probability

The probability of a single event equals the number of favorable outcomes divided by the total number of equally likely outcomes. Rolling a 3 on a fair six-sided die gives P = 1/6 ≈ 0.1667, or about 16.67%. The result always falls between 0 (impossible) and 1 (certain).

When events are not equally likely, you must know or estimate each outcome's probability directly rather than counting outcomes. This calculator assumes equally likely outcomes for the single-event mode.

Compound probability for independent events

Two events are independent when the outcome of one does not affect the other. For independent events, the AND rule multiplies their probabilities: P(A and B) = P(A) × P(B). The OR rule adds them and subtracts the overlap: P(A or B) = P(A) + P(B) − P(A) × P(B).

For example, the probability of flipping heads (0.5) and rolling a 6 (0.1667) is 0.5 × 0.1667 ≈ 0.0833. The probability of at least one of those events is 0.5 + 0.1667 − 0.0833 ≈ 0.5833.

Complementary probability

The complement of an event is everything that is not that event. P(not A) = 1 − P(A). If the probability of rain is 0.3, the probability of no rain is 0.7. Complementary probability is useful when it is easier to calculate what you do not want than what you do.