Probability Calculator
Enter the chance of event A and event B as percentages, and the number of times you try A. You get the chance of both, either, neither or exactly one, and the chance of at least one A over several trials.
Your numbers
How we calculate it
For independent events, one result does not change the other. With a = chance of A and b = chance of B, as decimals: both = a × b, either = a + b − a × b, neither = (1 − a) × (1 − b), and exactly one = a × (1 − b) + b × (1 − a).
The chance of at least one A in n tries is 1 − (1 − a)^n. For A at 50% and B at 30%, both is 15%, either is 65%, neither is 35% and exactly one is 50%. The chance of at least one A in 3 tries is 87.5%.
Assumptions and limits
- This works only when the events are independent. Drawing cards without putting them back, for example, is not independent.
- Chances must be between 0% and 100%.
- The number of trials can be up to 1,000,000.
Frequently asked questions
What are independent events?
Events are independent when one happening does not change the chance of the other. Two coin flips are independent, because the first flip does not affect the second.
How do I find the chance of at least one success?
Work out the chance of no successes in every try, then subtract it from 1. If one try succeeds 50% of the time, the chance of no success in 3 tries is 0.5 × 0.5 × 0.5 = 12.5%, so at least one success is 87.5%.
What is the difference between and, or and exactly one?
Both means A and B happen. Either means at least one of them happens, including both. Exactly one means one happens and the other does not.
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Worked example (a fixed example using the starting numbers, it does not change as you type)
Inputs: Chance of A (%) = 50; Chance of B (%) = 30; Number of trials for A = 3.
- A and B 15%
- A or B 65%
- Neither A nor B 35%
- Exactly one of A or B 50%
- At least one A in n trials 87.5%
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