Probability Calculator
Pick the kind of probability you need and enter your numbers. The calculator gives the answer as a decimal and a percent, with odds and the full working for one event, A and B, A or B, A given B and repeated trials.
Last updated November 3, 2026
A whole number, such as 3 for 3 red marbles.
A whole number of 1 or more.
Result
P = 3/10 = 0.3 (30%).
| Measure | Value |
|---|---|
| Decimal | 0.3 |
| Percent | 30% |
| Simplified fraction | 3/10 |
| Odds for | 3 : 7 |
| Odds against | 7 : 3 |
| Chance it does not happen | 70% |
Show the work
Formula: P = favorable outcomes ÷ total outcomes; odds for = favorable : (total − favorable)
- Entered: 3 favorable out of 10 total.
- P = 3 ÷ 10 = 0.3, which is 30%.
- Fraction in lowest terms: 3/10.
- Unfavorable outcomes: 10 − 3 = 7, so odds for are 3 : 7 in lowest terms.
Result: P = 3/10 = 0.3 (30%).
The probability formulas
P = favorable ÷ total P(not A) = 1 − P(A) P(A and B) = P(A) × P(B) P(A or B) = P(A) + P(B) − P(A and B)
A probability is a number from 0 to 1, where 0 means impossible and 1 means certain. When all outcomes are equally likely, divide the number of favorable outcomes by the total number of outcomes. Multiply by 100 for a percent.
The complement is the chance an event does not happen. Because something must occur, P(not A) = 1 − P(A). Multiplying P(A) and P(B) gives the chance both happen, but only when the events are independent. If A and B cannot happen together, they are mutually exclusive and P(A or B) is simply P(A) + P(B).
Conditional probability asks how likely A is once B is known to have happened: P(A | B) = P(A and B) ÷ P(B). It needs P(B) to be greater than 0.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Combination Calculator, Percentage Calculator and Statistics Calculator.
Odds, fractions and percents
Odds compare favorable outcomes with unfavorable ones. With 3 favorable outcomes out of 10, the probability is 3/10, but the odds for are 3 : 7. The calculator reduces both to lowest terms, so 2 out of 8 reads as 1/4 and odds of 1 : 3.
Probability and odds describe the same chance differently, so do not mix them up: odds of 1 : 3 mean a probability of 1/4, not 1/3.
Independent, exclusive or overlapping
Two events are independent when one has no effect on the chance of the other, such as two separate coin flips. Drawing two cards without putting the first back is not independent, because the first draw changes what is left.
For overlapping events, the sum P(A) + P(B) counts the overlap twice, so one copy of P(A and B) is subtracted. The overlap cannot be any size: it must be at least P(A) + P(B) − 1 (and never below 0) and no more than the smaller of the two probabilities. The calculator checks this and reports an error if your three numbers cannot all be true.
Repeated trials
For n independent tries with the same success chance p, the chance of exactly k successes is C(n, k) × p^k × (1 − p)^(n − k), where C(n, k) counts the ways to choose which tries succeed. This is the binomial distribution. The calculator accepts up to 1,000 trials.
The chance of at least one success is 1 − (1 − p)^n, the complement of every try failing. For example, at least one six in four rolls of a fair die is 1 − (5/6)^4 = 0.517747, slightly better than even.
Common mistakes to avoid
Multiplying probabilities for events that are not independent gives the wrong answer. A run of five heads does not make tails more likely on the next flip, but it also does not make the five flips together more probable than any other specific sequence.
Another frequent error is entering a percent where a decimal is expected. Use the setting above the fields to choose decimals or percents, and the result is shown in both forms.
How to use the Probability Calculator
- Choose the type of probability: single event, complement, A and B, A or B, conditional or repeated trials.
- Enter the counts or probabilities, as decimals or percents.
- Read the result as a decimal, a percent and, for one event, as a fraction and odds.
- Open Show the work to see each calculation, then Copy, Print or Share.
Worked example
Flip a fair coin 5 times. The chance of exactly 3 heads is C(5, 3) × 0.5³ × 0.5² = 10 × 0.125 × 0.25 = 0.3125, or 31.25%. The chance of at least one head is 1 − 0.5⁵ = 0.96875.
| Question | Calculation | Answer |
|---|---|---|
| 3 red out of 10 marbles | 3 ÷ 10 | 0.3 (30%) |
| A and B, independent, 0.5 and 0.4 | 0.5 × 0.4 | 0.2 |
| A or B, overlap 0.2 | 0.5 + 0.4 − 0.2 | 0.7 |
| A given B, P(A and B) = 0.2, P(B) = 0.4 | 0.2 ÷ 0.4 | 0.5 |
| At most 3 heads in 10 flips | sum for 0 to 3 | 0.171875 |
| At least one six in 4 rolls | 1 − (5/6)⁴ | 0.517747 |
Frequently asked questions
What is the difference between probability and odds?
Probability compares favorable outcomes with all outcomes, while odds compare favorable with unfavorable. A probability of 1/4 is odds of 1 to 3.
How do I know if two events are independent?
They are independent if knowing that one happened does not change the chance of the other, as with separate coin flips or dice rolls.
Why can my P(A and B) be rejected?
The overlap cannot exceed the smaller probability and cannot be below P(A) + P(B) − 1, so some combinations of numbers are impossible.
Can I enter percents instead of decimals?
Yes. Choose percents in the setting above the fields and type 40 for 40%; the answer appears as both a decimal and a percent.
What does at least one success mean?
It means one or more successes in your trials, which is 1 minus the chance that every single trial fails.