Probability Calculator
Combined probability of independent events.
Enter your values
ⓘ Live results
Results
- Both A and B
- 13.5%
- A or B (either)
- 61.5%
- Neither
- 38.5%
- A at least once in 5 trials
- 83.193%
- Odds of A
- 0.429 to 1
Quick answer
For independent events, P(A and B) = P(A)·P(B) and P(A or B) = P(A) + P(B) − P(A)·P(B).
P(A∩B) = P(A)·P(B)
How to use the Probability Calculator
- 1Enter the probability of each event as a percentage.
- 2Set repeated trials if you want the 'at least once' figure.
- 3Read the combined probabilities.
Worked example
Using the values the calculator loads with:
Inputs
- Probability of A30 %
- Probability of B45 %
- Repeated trials of A5
Results
- Both A and B13.5%
- A or B (either)61.5%
- Neither38.5%
- A at least once in 5 trials83.193%
- Odds of A0.429 to 1
Frequently asked questions
What does independent mean?
One event's outcome doesn't change the other's probability. Two coin flips are independent; drawing cards without replacement is not.
Why is 'at least once' so high?
Failure has to happen every single time, and (1−p)^n shrinks fast — a 10% chance over 20 tries is 88% likely to occur.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.