Combine two independent event probabilities — AND, OR, and NOT.
Assumes A and B are independent events.
Two events are independent when one happening doesn't change the chance of the other happening — like two separate coin flips. This calculator's AND/OR formulas only hold for independent events; dependent events (e.g. drawing cards without replacement) need a different, conditional formula.
Simply adding them would double-count the outcomes where both A and B happen. Subtracting P(A)×P(B) — the overlap — corrects for that double-count, which is why the OR formula is P(A) + P(B) − P(A)×P(B).
P(not A) only looks at event A and equals 1 − P(A). P(neither A nor B) requires both events to fail at once, which for independent events equals P(not A) × P(not B) — a smaller probability than either individual complement.