Probability Calculator

Calculate the union, intersection, and complement of two independent events, or the probability of a range under a normal distribution.

Probability of Two Independent Events

Enter P(A) and P(B) as values between 0 and 1.

Probability of a Normal Distribution

Find the area (probability) between two bounds on a normal distribution curve.

Use "-inf" or "inf" for an unbounded side.

Independent events, explained

Two events are independent if one occurring doesn't change the probability of the other. For independent events, the probability of both happening is just P(A) × P(B) — that's the intersection. The union (A or B or both) is P(A) + P(B) minus the intersection, since otherwise the overlap would be counted twice.

Why the normal distribution matters

Many real-world measurements — heights, test scores, measurement errors — cluster around an average in a predictable bell-curve pattern. The normal distribution calculator converts your bounds into z-scores (how many standard deviations from the mean) and finds the area under the curve between them, which corresponds to the probability of a value falling in that range.

P(A Δ B), the "exclusive or," means A or B happens but not both simultaneously — it's the union minus twice the intersection, removing the overlap entirely rather than counting it once.

Common questions

What if my events aren't independent?

Then you need conditional probability — P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of B given that A already happened. This calculator's "two independent events" tool assumes no such dependency.

Why use z-scores for the normal distribution?

Every normal distribution has a different mean and spread, but converting to z-scores (standard deviations from the mean) maps any of them onto the same standard normal curve, so one set of probability tables (or one formula) works for all of them.

More Math Calculators

Pick another tool to jump straight to it.