Probability Calculator

The Basic Probability Formula

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain) — often written as a percentage. For a single event with equally likely outcomes, it's a simple ratio:

Rolling a 4 on a standard six-sided die: there's 1 favorable outcome (the face showing 4) out of 6 total possible outcomes, so P(4) = 1/6 ≈ 16.67%. This only works cleanly when every outcome is equally likely — a loaded die or a biased coin needs a different approach (the actual observed frequency, not a theoretical count).

Combining Two Events: AND vs. OR

Real problems usually involve more than one event, and the two most common questions are "what's the chance BOTH happen" and "what's the chance AT LEAST ONE happens":

• P(A and B), independent events: P(A) × P(B) — e.g. flipping heads twice in a row: 0.5 × 0.5 = 0.25.
• P(A or B), independent events: P(A) + P(B) − P(A and B) — you subtract the overlap so it isn't double-counted.
• P(A or B), mutually exclusive events: just P(A) + P(B) — since the events can't both happen, there's no overlap to subtract (e.g. rolling a 2 or a 5 on one die roll — you can't roll both at once).

Mixing these up is the most common mistake — using the mutually-exclusive OR formula on events that can actually overlap will overstate the probability, since you haven't removed the double-counted overlap.

How to Use This Calculator

• Single Event tab: enter favorable outcomes and total possible outcomes for a straightforward ratio.
• Two Events tab: enter P(A) and P(B) as decimals (0 to 1) — tick "mutually exclusive" if the two events can't both happen.
• Complement tab: enter P(A) to instantly get P(not A) = 1 − P(A).
• For repeated trials with a fixed success probability (coin flips, pass/fail attempts), use the dedicated Binomial Probability Calculator instead — it handles multi-trial scenarios this tool doesn't.

Frequently Asked Questions