Probability Calculator
Work out single-event probability and odds, plus independent two-event combinations (both, either, neither).
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What this tool does
Work out single-event probability and odds, plus independent two-event combinations (both, either, neither). Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
How to use the Probability Calculator
- Enter or select favourable outcomes.
- Enter or select total possible outcomes.
- Enter or select probability of event a (%).
- Enter or select probability of event b (%).
- Read the calculated result; change any measurement to compare alternatives.
Formula
single probability = favourable / total; independent events: P(A and B) = P(A)×P(B); P(A or B) = P(A) + P(B) − P(A)×P(B); two draws without replacement both favourable = f/t × (f−1)/(t−1)
- fav
- Favourable outcomes
- total
- Total possible outcomes
- pa
- Probability of event A (%)
- pb
- Probability of event B (%)
Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
Worked example
For probability calculator, the following measurements illustrate the exact method: Favourable outcomes: 3; Total possible outcomes: 10; Probability of event A (%): 40; Probability of event B (%): 30.
Inputs
- Favourable outcomes3
- Total possible outcomes10
- Probability of event A (%)40
- Probability of event B (%)30
Result
- Single-event probability (%)30
- Odds in favour3 : 7
- P(A and B) — independent (%)12
- P(A or B) — independent (%)58
- P(neither A nor B) (%)42
- P(both draws favourable, without replacement) (%)6.67
Results explained
- Single-event probability (%)
- Single-event probability (%) from the formula above. Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
- Odds in favour
- Odds in favour from the formula above. Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
- P(A and B) — independent (%)
- P(A and B) — independent (%) from the formula above. Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
- P(A or B) — independent (%)
- P(A or B) — independent (%) from the formula above. Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
- P(neither A nor B) (%)
- P(neither A nor B) (%) from the formula above. Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
- P(both draws favourable, without replacement) (%)
- P(both draws favourable, without replacement) (%) from the formula above. Compound results assume A and B are independent. The without-replacement result assumes two draws from the same finite pool described by the favourable/total inputs.
Frequently asked questions
Divide the number of favourable outcomes by the total number of equally likely outcomes. Rolling a 3 on one fair die is 1 favourable outcome out of 6, so the probability is 1/6 ≈ 16.67%.
Probability compares favourable outcomes with all outcomes (3 of 10 = 30%). Odds compare favourable with unfavourable outcomes (3 : 7). The same event can be stated either way; do not mix the two denominators.
Only when the events are independent — one outcome does not change the other's chances, like two separate coin flips. For dependent events (drawing cards without replacement) the second probability must be adjusted for what was removed.
Adding double-counts the overlap where both happen. Subtracting P(A)×P(B) once (for independent events) counts that overlap exactly once. If the events are mutually exclusive the overlap is zero and simple addition is correct.
No. Probabilities run from 0 (impossible) to 1, or 0% to 100% (certain). A result outside that range means an input or an independence assumption is wrong.