Probability Calculator

Choose a probability rule and enter your known probabilities to calculate the result.

How to Use the Probability Calculator

Choose which probability rule applies — independent events, mutually exclusive, conditional, and so on — before entering the individual probabilities, since each rule combines them differently.

Complement:              P(not A) = 1 − P(A)
A and B (independent):   P(A and B) = P(A) × P(B)
A or B (mutually excl.): P(A or B) = P(A) + P(B)
A or B (independent):    P(A or B) = P(A) + P(B) − P(A) × P(B)

Four rules, and which one applies depends entirely on whether two events can influence each other and whether they can happen simultaneously. This Probability Calculator covers all four. Independent means one event's outcome doesn't touch the other's odds at all — two separate coin flips, say. Drawing two cards from a deck without replacement isn't independent, and this calculator's simple multiplication won't get you the right answer there; that needs conditional probability instead.

The subtraction in the "or, not mutually exclusive" formula exists to fix double-counting — adding P(A) and P(B) straight up counts the overlap (both happening at once) twice, so subtracting P(A)×P(B) corrects for it. Mutually exclusive events have zero overlap by definition, which is exactly why their formula skips that step.