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Probability measures how likely something is, on a scale from 0 (impossible) to 1 (certain). For a single event it's the favorable outcomes divided by all possible outcomes; for two events it depends on whether you want both, or either.
Choose the case, enter the numbers, and get the probability as a decimal and a percentage.
Probability Calculator: step-by-step worked example
Chance of drawing an ace from a 52-card deck (4 aces).
- Calculation
- Single event (favorable / total)
- Favorable outcomes
- 4
- Total outcomes
- 52
- 1
Favourable ÷ total outcomes
P = Favourable ÷ Total
4 ÷ 52 = 0.0769
- 2
As a percentage
P × 100
0.076923 × 100 = 7.6923%
- 3
Probability it does not happen
P(not) = 1 − P
1 − 0.076923 = 0.9231
- 4
“1 in k” form
k = Total ÷ Favourable
52 ÷ 4 = 1 in 13
- Favourable47.7%
- Other4892.3%
Good to know: Classical probability assumes all outcomes are equally likely. For two independent events both happening, multiply (P(A) × P(B)); for “at least one”, use P(A) + P(B) − P(A) × P(B).
Probability Calculator — how it works
The three cases
| Case | Formula |
|---|---|
| Single event | favorable ÷ total |
| Both A and B (independent) | P(A) × P(B) |
| Either A or B (independent) | P(A) + P(B) − P(A) × P(B) |
Probabilities are entered as decimals between 0 and 1 (0.5 = 50%).
Why "or" subtracts the overlap
Adding P(A) and P(B) double-counts the cases where both happen, so you subtract P(A)×P(B) once to correct it. Without that term, two 60% events would give a nonsensical 120% chance of at least one.
Independent vs dependent
The AND and OR formulas here assume the events are independent — one doesn't affect the other, like two separate coin flips. If drawing without replacement or when one event changes the odds of the next, the events are dependent and the multiplication rule needs conditional probabilities instead.
The complement trick
The chance an event does NOT happen is 1 − P. This is often the easy route to "at least one" problems: the chance of at least one success is 1 minus the chance of all failures. The tool reports the complement alongside the result.
Worked example
Rolling a die, the chance of a 6 is a single event: 1 favorable ÷ 6 total ≈ 0.167 (16.7%). Rolling two dice, the chance of a 6 on both is P(A) × P(B) = 0.167 × 0.167 ≈ 0.028 (2.8%). The chance of a 6 on at least one is 0.167 + 0.167 − 0.028 ≈ 0.306 (30.6%) — not simply doubled, because the both-sixes case is only counted once.
Frequently asked questions
How do I calculate probability?+
For a single event, divide the number of favorable outcomes by the total number of possible outcomes. Rolling a 6 on a die is 1 ÷ 6 ≈ 0.167, or 16.7%.
How do I find the probability of two events both happening?+
For independent events, multiply their probabilities: P(A and B) = P(A) × P(B). Two coin heads in a row is 0.5 × 0.5 = 0.25.
How do I find the probability of either event?+
P(A or B) = P(A) + P(B) − P(A) × P(B). The final term removes the double-counted overlap where both occur.
What does independent mean?+
Two events are independent when one does not change the probability of the other, like separate dice rolls. The AND/OR formulas here assume independence.
What is the complement of a probability?+
It is the chance the event does NOT happen, equal to 1 − P. It’s the shortcut for "at least one" problems: 1 minus the chance that none occur.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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