Probability measures how likely something is, from 0 (impossible) to 1 (certain). For a single event the key rule is the complement: P(not A) = 1 − P(A). For two independent events — where one doesn't affect the other — you multiply for "and" (P(A and B) = P(A)·P(B)) and add then subtract the overlap for "or" (P(A or B) = P(A)+P(B)−P(A)·P(B)). Those few rules cover most everyday probability questions, as long as you check that the events really are independent.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the standard rules of probability for independent events.
The probability rules
Every probability sits between 0 and 1. "And" means both events occur, so for independent events you multiply — each condition shrinks the chance. "Or" means at least one occurs; you add the two probabilities but subtract their overlap (counted twice in the sum) to avoid double counting. The chance that neither occurs is the product of the two complements, and it gives a quick route to "at least one": P(at least one) = 1 − P(neither).
Worked example — two independent events
Scenario: P(A) = 0.5 and P(B) = 0.2, independent.
Both events together have a 10% chance; at least one has a 60% chance; neither happens 40% of the time; and A alone fails to happen half the time. Notice the consistency check: P(A or B) + P(neither) = 0.60 + 0.40 = 1, exactly as it must, since "at least one" and "neither" are complements. Change P(B) and the figures scale predictably — a smaller B lowers both the "and" and the "or", as the table above shows.
Frequently Asked Questions
Likelihood from 0 (impossible) to 1 (certain). Favourable ÷ total for equally likely outcomes.
Independent: multiply. 0.5 × 0.2 = 0.10. Mutually exclusive: 0.
P(A)+P(B)−P(A)·P(B) = 0.5+0.2−0.10 = 0.60. Subtract the overlap.
not A = 1 − P(A). Neither = (1−A)(1−B). At least one = 1 − neither.
One event doesn't affect the other (separate coin flips). Dependent events need conditional probability.