Free probability calculator
Calculate the probability of an event — enter favorable outcomes and total outcomes to see probability as a fraction, decimal, and percentage, updated live, as you type.
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Independent events assumed. P(A AND B) = P(A) × P(B).
Results are estimates. Consult a professional.
How the probability calculator works
Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain) — or equivalently as a percentage. The classical definition divides the number of favourable outcomes by the total number of equally likely outcomes.
Worked example: rolling a standard six-sided die
A fair six-sided die has faces {1, 2, 3, 4, 5, 6}. Even faces = {2, 4, 6}. Faces greater than 4 = {5, 6}. Both even AND > 4 = {6}.
Common probability values — dice, coins, and cards
These benchmark probabilities are useful for checking your intuition and verifying more complex calculations.
| Event | Favourable / Total | Probability |
|---|---|---|
| Coin: heads | 1/2 | 0.500 |
| Die: rolling a 6 | 1/6 | 0.167 |
| Die: rolling > 4 | 2/6 | 0.333 |
| Die: rolling even | 3/6 | 0.500 |
| Two dice: sum = 7 | 6/36 | 0.167 |
| Two dice: sum = 12 | 1/36 | 0.028 |
| Card: drawing an ace | 4/52 | 0.077 |
| Card: drawing a heart | 13/52 | 0.250 |
| Card: red face card | 6/52 | 0.115 |
Source: classical probability with equally likely outcomes
Tips for calculating probability
Probability is intuitive to mis-apply. These principles help you set up problems correctly before plugging in numbers.
- List the sample space first — write out all possible outcomes before counting favourable ones; this prevents double-counting or omissions.
- Check for independence before using P(A)×P(B) — drawing two cards without replacement makes the second draw dependent on the first; use conditional probability instead.
- Complement rule saves steps — P(at least one 6 in 3 rolls) = 1 − P(no 6 in 3 rolls) = 1 − (5/6)³ ≈ 0.421; this is faster than summing three cases.
- Mutually exclusive vs independent — if A and B cannot both occur (mutually exclusive), P(A∩B) = 0, so P(A∪B) = P(A)+P(B); but they are NOT independent (knowing A occurred tells you B didn't).
- Convert between fractions, decimals, and percentages — all three express the same quantity; fractions keep precision; decimals ease arithmetic; percentages aid communication.
Accuracy and limitations
This calculator uses exact rational arithmetic when inputs are whole numbers, so P(3/6) is stored as the exact fraction 1/2 before any decimal conversion. For decimal inputs (e.g. 0.37), standard IEEE 754 double precision applies — results are accurate to approximately 15 significant digits. The classical probability model assumes equally likely outcomes; it does not apply to unfair coins, weighted dice, or real-world events where outcomes have unequal likelihoods. For those cases, use empirical or subjective probability from observed data or expert estimates.
Key terms
About this calculator
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