Independent Events Probability Calculator

About this calculator

Two events are statistically independent when the outcome of one has no effect on the probability of the other — flipping a coin twice, or rolling a die and drawing a card from a separate deck, are classic examples. For independent events A and B, the multiplication rule gives P(A and B) = P(A) × P(B); the addition rule gives P(A or B) = P(A) + P(B) − P(A) × P(B) to avoid double-counting the overlap; and the probability that neither happens is P(not A) × P(not B), since independence of A and B also implies independence of their complements.

These formulas underpin risk analysis (the odds that two unrelated system components both fail), quality control (the chance that two independently inspected batches both pass), genetics (probability that a child inherits two independently-assorting traits), and everyday reasoning about compound events like the odds of it raining and your flight being delayed on the same day. Confusing independent events with mutually exclusive ones is a common mistake — mutually exclusive events can never both happen, so P(A and B) = 0, which is the opposite situation from independence.

This calculator takes the individual probabilities of two independent events and returns P(A and B), P(A or B), and P(neither) in one step.