Probability Calculator
Calculate the probability of a single event from a fraction or percentage, including its complement and odds. Or enter up to five independent events and find the probability that all occur, at least one occurs, or none occur. Results update instantly as you type.
How It Works
Probability is a measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). It can also be expressed as a percentage between 0% and 100%.
Single Event Probability:
When you know the number of favourable outcomes and the total number of equally likely outcomes:
P(event) = Favourable outcomes ÷ Total outcomes
Example: Drawing a red card from a standard 52-card deck. There are 26 red cards, so P = 26 ÷ 52 = 0.5 (50%).
From a probability P, you can derive:
Complement (probability event does NOT occur) = 1 − P
Odds in favour = P : (1 − P), simplified
Odds against = (1 − P) : P, simplified
Example: P = 3/12 = 0.25. Complement = 0.75. Odds in favour = 1:3. Odds against = 3:1.
Multiple Independent Events:
When events are independent (the outcome of one does not affect the others), you can combine their individual probabilities.
P(all events occur) = P1 × P2 × P3 × ... (multiply all probabilities together)
P(at least one occurs) = 1 − P(none occur)
P(none occur) = (1 − P1) × (1 − P2) × (1 − P3) × ...
Worked example: Three events with probabilities 0.5, 0.3, and 0.8.
P(all) = 0.5 × 0.3 × 0.8 = 0.12 (12%)
P(none) = 0.5 × 0.7 × 0.2 = 0.07 (7%)
P(at least one) = 1 − 0.07 = 0.93 (93%)
Important: These formulas apply only to independent events. If events are correlated (e.g. rolling two dice where the second result depends on the first — it does not in this case, but conditional events do exist), different formulas are needed. This calculator assumes full statistical independence.
Frequently Asked Questions
What is the complement of a probability?
The complement is the probability that an event does NOT happen. Since something must either happen or not happen, P(event) + P(complement) = 1. If there is a 25% chance of rain, there is a 75% chance of no rain. This is one of the most useful rules in probability.
What are "odds" vs "probability"?
Probability is expressed as a fraction of all outcomes (e.g. 1/4 = 0.25). Odds express the ratio of favourable to unfavourable outcomes (e.g. 1:3, meaning one favourable outcome for every three unfavourable ones). Betting markets use odds; probability theory uses the 0–1 scale. This calculator shows both.
What does "independent events" mean?
Two events are independent if the outcome of one has no effect on the probability of the other. Flipping a coin twice is independent — the first flip does not affect the second. Drawing two cards without replacement is NOT independent — the first draw changes the deck. The multiple-event mode assumes full independence.
Can I enter probability as a percentage?
Yes. In the single event mode you can enter the number of favourable outcomes and total outcomes, or switch to percentage entry. In the multiple events mode each event accepts a percentage value (0–100).
Why is P(at least one) so high even when individual probabilities are low?
Because P(at least one) = 1 − P(none), and P(none) shrinks rapidly as you add more events. If five independent events each have a 20% chance, P(none) = 0.8^5 ≈ 0.328, so P(at least one) ≈ 67.2% — much higher than any single event alone. This is why many small risks compound into a significant aggregate risk.