Probability Calculator — chance of an event from outcomes

How it works

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). For situations where every outcome is equally likely — a fair coin, a balanced die, a well-shuffled deck — the classical rule is simply a count:

P = favorable outcomes ÷ total outcomes

Count how many outcomes make the event happen (the favorable ones), divide by how many outcomes there are in total, and you have the probability. Multiply by 100 to read it as a percentage. The complement — the chance the event does not happen — is whatever is left over, 1 − P, since something must occur.

Worked example

What's the probability of drawing a heart from a standard 52-card deck? There are 13 hearts (favorable) out of 52 cards (total):

P = 13 ÷ 52 = 0.25 = 25%

So there's a 25% chance, and a 75% chance of not drawing a heart (1 − 0.25). Other equally-likely examples: rolling an even number on a die is 3 ÷ 6 = 0.5 (50%), and flipping heads is 1 ÷ 2 = 0.5. A certain event (rolling 1–6 on a die) is 6 ÷ 6 = 1, and an impossible one is 0.

Frequently asked questions

How do I calculate probability?

Divide the number of favorable outcomes by the total number of possible outcomes, assuming each is equally likely. Drawing an ace from a deck is 4 ÷ 52 ≈ 0.077, or about 7.7%. Make sure you count *all* equally-likely outcomes for the total.

What's the complement, and why does it matter?

The complement is the probability the event does **not** happen, equal to 1 − P. It's useful because some events are easier to count the other way round — the chance of "at least one" success is often found as 1 minus the chance of "none". Probability and complement always add to 1.

Can a probability be more than 1 or negative?

No — a valid probability is always between 0 and 1 (0% and 100%). If a calculation gives more than 1, you've likely counted more favorable outcomes than total outcomes, or double-counted. 0 means impossible, 1 means certain, and everything real lies in between.

What does "equally likely" mean, and what if outcomes aren't?

The classical formula assumes every outcome has the same chance — true for fair dice, coins and shuffled cards. If outcomes aren't equally likely (a weighted die, say), you can't just count; you add up the individual probabilities of the favorable outcomes instead. This calculator covers the equally-likely case.

How is probability different from odds?

Probability compares favorable outcomes to the **total** (13 out of 52 = 0.25). Odds compare favorable to **unfavorable** (13 to 39, or 1 to 3). They describe the same situation: odds of "a to b" correspond to a probability of a ÷ (a + b).

How do I combine probabilities of two events?

It depends on the relationship. For independent events both happening, multiply (P(A) × P(B)); for either of two mutually exclusive events, add. This page handles a single event; combined and repeated-trial cases — like the chance of k successes in n tries — are covered by the binomial distribution calculator.