Probability Calculator
Calculate single event probability, complementary probability, and odds for/against an event.
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How to use this calculator
Probability ranges from 0 (impossible) to 1 (certain). Expressed as fraction, decimal, or percentage.
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Enter the number of favourable outcomes (the event you are interested in).
- 2
Enter the total number of possible outcomes.
- 3
Optionally enter the number of trials for the "at least one success" calculation.
Frequently asked questions
What is probability?
Probability measures how likely an event is to occur, expressed as a number between 0 and 1. P=0 means impossible; P=1 means certain. P=0.5 means equally likely to happen or not.
What is the difference between probability and odds?
Probability = favourable / total. Odds (for) = favourable : unfavourable. A probability of 1/4 = odds of 1:3. Odds are common in gambling; probability is used in statistics.
What is complementary probability?
The probability that an event does NOT happen = 1 − P(event). If P(rain) = 0.3, then P(no rain) = 0.7.
How do I find the probability of at least one success?
P(at least one) = 1 − P(none). P(none in n trials) = (1-p)^n. So P(at least one) = 1 − (1-p)^n. Example: rolling a 6 at least once in 4 rolls = 1 − (5/6)^4 ≈ 51.8%.
Probability fundamentals
Classical probability
Classical probability assumes all outcomes are equally likely. P(A) = favourable outcomes / total outcomes. Rolling a fair die: P(rolling a 3) = 1/6. Flipping a fair coin: P(heads) = 1/2. Drawing a heart from a deck: P = 13/52 = 1/4.
Probability vs. statistics
Probability works forward: given a known model, predict outcomes. Statistics works backward: given observed outcomes, estimate the model. If you know a die is fair (model), probability predicts each face has a 1/6 chance. If you observe 1,000 rolls, statistics estimates whether the die is fair.
Real-world probability examples
Medical tests: P(disease | positive test). Insurance: P(accident in a year). Finance: P(market down >10% in a year). Weather: P(rain tomorrow). Quality control: P(defective part). Probability underpins decision-making in medicine, engineering, business, and science.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →