Probability Calculator
(Two Events, Single Events and Repeated Tries)
Enter P(A) and P(B) and say how the events are related, or work out a single event from counts, or the chance of something happening at least once.
What do you want to work out?
As 0.3, 30% or 3/10. Numbers above 1 are read as percentages
How are A and B related?
Two Events
💡 Formula Guide
This probability calculator handles two events, a single event from counts, and the chance of something happening at least once in repeated tries. Probabilities can be typed as decimals, percentages or fractions.
Two Events: And, Or, Given
| Result | Independent | Mutually exclusive | P(A and B) = 0.1 |
|---|---|---|---|
| P(A and B) | 0.15 | 0 | 0.10 |
| P(A or B) | 0.65 | 0.80 | 0.70 |
| P(exactly one) | 0.50 | 0.80 | 0.60 |
| P(neither) | 0.35 | 0.20 | 0.30 |
| P(A given B) | 0.30 | 0 | 0.20 |
All three columns use P(A) = 0.3 and P(B) = 0.5. Only P(A and B) changes, and every other result follows from it. That is why the calculator asks how the events are related instead of assuming independence. Many tools multiply P(A) × P(B) for every pair, which is only right when the events are independent.
One Event From Counts
Drawing an ace from a 52-card deck has 4 favourable outcomes, so the probability is 4 ÷ 52 = 7.69%, about 1 in 13. The odds against are 48 to 4. This rule needs every outcome to be equally likely.
At Least Once in Repeated Tries
The chance of no six in one roll is 5/6. In 10 rolls it is (5/6)^10 = 16.15%, so the chance of at least one six is 83.85%. Four rolls are enough for a better than even chance. Adding the chances (10 × 1/6) gives 1.67, which is the expected number of sixes, not a probability.
For the chance of exactly k successes, or at most k, use the Binomial Probability Calculator.
How to Use the Probability Calculator
- Choose a mode: Pick two events, one event from counts, or at least once in repeated tries.
- Enter the probabilities: Type them as decimals, percentages or fractions, such as 0.3, 30% or 3/10.
- Say how A and B are related: Choose independent, mutually exclusive, or enter P(A and B) yourself if the events depend on each other.
- Read the results: The calculator shows every combination at once, as a percentage and a decimal.
Frequently Asked Questions
How do I find the probability of A or B?
Use P(A or B) = P(A) + P(B) − P(A and B). For independent events with P(A) = 0.3 and P(B) = 0.5, P(A and B) = 0.15, so P(A or B) = 0.65.
How do I find the probability of A and B?
For independent events, multiply: P(A) × P(B). For mutually exclusive events it is 0. If the events depend on each other, you need P(A and B) from the data, or P(A) × P(B given A).
What is conditional probability?
It is the chance of A when B is known to have happened: P(A given B) = P(A and B) ÷ P(B). With P(A and B) = 0.1 and P(B) = 0.5, P(A given B) = 0.2.
What is the chance of something happening at least once?
Take 1 minus the chance it never happens: 1 − (1 − p)^n. The chance of rolling at least one six in 10 rolls of a die is 1 − (5/6)^10 = 83.85%.
What is the difference between independent and mutually exclusive?
Independent events do not affect each other, so both can happen. Mutually exclusive events cannot happen together, so P(A and B) is 0. Two events with non-zero probability cannot be both.
Why does the calculator say my numbers are not possible?
P(A and B) can be no larger than the smaller of P(A) and P(B), and no smaller than P(A) + P(B) − 1. A value outside that range cannot come from real events.
Formulas and worked examples checked in October 2026.