Probability Calculator

Calculate probabilities for two independent events — union, intersection, complements, and repeated trials.

Modify the values and click the Calculate button to use this tool.

Probability of Two Events

Enter P(A) and P(B) to find all related probabilities for independent events.

Values must be between 0 and 1.

Modify the values and click the Calculate button to use this tool.

Probability Solver for Two Events

Provide any 2 values below to calculate the rest (independent events).

Modify the values and click the Calculate button to use this tool.

Probability of a Series of Independent Events

Key formulas

P(A∩B) = P(A)×P(B)
P(A∪B) = P(A)+P(B)−P(A∩B)

Probability of two events

Probability is a number between 0 and 1 representing the likelihood of an outcome. For independent events A and B, the probability of both occurring is the product of their individual probabilities.

P(A ∩ B) = P(A) × P(B)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

The complement P(A') = 1 − P(A). XOR (exactly one event) is P(A Δ B) = P(A ∪ B) − P(A ∩ B).

Complement of A and B

P(A') is the probability that event A does not occur. P((A∪B)') is the probability that neither A nor B occurs — equal to 1 − P(A∪B).

Series of independent events

When the same independent event repeats n times, the probability of all occurring is Pn. Example: P(rolling 6 five times) = (1/6)5.

Frequently Asked Questions

Independent events do not affect each other's probability. Outcome of A does not change P(B).

Probability is always from 0 (impossible) to 1 (certain). Use decimals: 50% = 0.5.