Calculate the probability of an event. This free probability calculator handles single events (favourable ÷ total) and two independent events (AND, OR, neither) — shown as a percentage, decimal, fraction and odds.
Probability of an event = favourable outcomes ÷ total outcomes. For one roll of a die landing on a 4: 1 ÷ 6.
Enter each probability as a decimal between 0 and 1. These results assume A and B are independent events.
Probability ranges from 0 (impossible) to 1 (certain), often shown as a percentage. The two-event results below assume independence — one event doesn’t affect the other.
How the Probability Calculator Works
Probability measures how likely an event is to happen, from 0 (impossible) to 1 (certain). This calculator handles a single event from favourable and total outcomes, and it also compares two independent events to find the chance both happen, either happens, or neither happens.
Formula: For a single event, Probability = favourable outcomes ÷ total possible outcomes (rolling a 4 on one die is 1 ÷ 6). For two independent events A and B, the calculator also derives: P(A and B) = P(A) × P(B), P(A or B) = P(A) + P(B) − (P(A) × P(B)), and P(neither) = (1 − P(A)) × (1 − P(B)).
- Favourable outcomes — the number of outcomes that count as a “win,” used in single-event mode
- Total possible outcomes — the total number of equally likely outcomes, used in single-event mode
- P(A) — the probability of event A, entered as a decimal between 0 and 1 in two-event mode
- P(B) — the probability of event B, entered as a decimal between 0 and 1 in two-event mode
Example Scenarios
| Favourable outcomes | Total outcomes | Probability |
|---|---|---|
| 1 | 6 | 16.67% (1/6) |
| 1 | 2 | 50% (1/2) |
| 3 | 4 | 75% (3/4) |
| 5 | 20 | 25% (1/4) |
| 2 | 8 | 25% (1/4) |
| 1 | 100 | 1% (1/100) |
Probability Calculator FAQ
How do I calculate the probability of rolling a specific number on a die?
Switch to single event mode, enter 1 as the favourable outcome and 6 as the total possible outcomes (assuming a standard six-sided die). The calculator returns 1 ÷ 6, or about 16.67%, along with the equivalent fraction and odds of 1 to 5 against.What’s the difference between “P(A or B)” and “P(A and B)”?
P(A and B) is the chance both events happen together, found by multiplying their probabilities. P(A or B) is the chance at least one of them happens, which adds the two probabilities and then subtracts the overlap (P(A) × P(B)) so it isn’t counted twice.Does this calculator work for dependent events?
No. The two-event mode assumes A and B are independent, meaning the outcome of one doesn’t affect the other’s probability. If your events are dependent (like drawing cards without replacement), these AND/OR/neither formulas won’t give an accurate answer.How do I convert a probability into odds?
In single event mode, odds are shown automatically as “favourable : against,” meaning favourable outcomes compared to the remaining outcomes, simplified to lowest terms. For example, 3 favourable out of 4 total shows as odds of 3 to 1 in favour.What does “P(neither)” mean in two-event mode?
P(neither) is the probability that neither event A nor event B happens. It’s calculated as the complement of each probability multiplied together: (1 minus P(A)) times (1 minus P(B)), reflecting both events failing to occur independently.Can I enter a probability greater than 1?
No. Probabilities in two-event mode must be entered as decimals between 0 and 1, since a probability represents a proportion of outcomes and can never exceed certainty (1) or fall below impossibility (0).Related Calculators
Curious how the odds behave over many trials? The dice roller lets you simulate real rolls to compare against the theoretical probability, while the standard deviation calculator helps you measure how much a set of outcomes actually varies. If your event involves fractions of outcomes, the fraction calculator can help you work through the arithmetic.