Probability Calculator

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

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%.

Counting the possibilities comes before weighing them. Our permutation and combination calculator handles ordered and unordered selections, and for a quick physical demonstration the dice roller and random number generator both work.

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.