Probability Calculator

Combine two independent event probabilities — AND, OR, or the complement.

P(A)

P(B)

Assumes A and B are independent events — the outcome of one doesn't affect the other.

Probability

15.00%

For independent events: P(A and B) multiplies the two probabilities; P(A or B) adds them and subtracts the overlap so it isn't double-counted.

A worked example

With P(A) = 50% and P(B) = 30%, both happening (A and B) comes to 15%, while either happening (A or B) comes to 65%.

Frequently asked questions

What does 'independent' mean here?

The outcome of one event has no effect on the other — like two separate coin flips. If events are dependent (one affects the other's likelihood), these formulas don't directly apply.

Why subtract P(A)×P(B) in the OR formula?

Simply adding P(A) and P(B) would double-count the outcomes where both happen — subtracting the overlap (P(A and B)) corrects for that double-counting.