Probability Calculator

What does this tool do?

This probability calculator gives you the core probabilities for two independent events (A and B) at a glance: both happening, either happening, neither happening, and their complements. It is handy for students working through probability homework, analysts assessing risk, and anyone making sense of games or odds.

How to use it

1. Enter your values into the fields.
2. The result is calculated instantly.
3. Read or copy the result.

The formulas for independent events

When events are independent, the tool applies these rules: P(A and B) = P(A)×P(B), P(A or B) = P(A)+P(B)−P(A and B), P(not A) = 1−P(A), and P(neither) = (1−P(A))×(1−P(B)). The multiplication rule only holds when the events do not affect each other—two separate dice rolls are independent, while drawing cards without replacement is dependent and must be computed differently.

Entering values correctly

Enter P(A) and P(B) as decimals between 0 and 1: type 0.25 for 25%, 0.70 for 70%. Values outside that range produce no result because they cannot represent a valid probability. The conditional column P(A | B) equals P(A) here precisely because the events are independent—a built-in visual reminder of what independence actually means.

Frequently asked questions