About At Least One Probability Calculator
This calculator finds the probability of at least one success in n independent trials, such as at least one six in four rolls. It calculates the chance of none and subtracts it from 1. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The same page also gives the exact number of successes k, at most k and at least k, using the binomial distribution. It opens with a one in six chance and four trials.
How to use At Least One Probability Calculator
- Choose a calculation: Two events, Conditional, Bayes' theorem or Repeated trials.
- Enter the probabilities as decimals, percentages or fractions, such as 0.4, 40% or 2/5.
- For two events, say how A and B are related: independent, mutually exclusive, or P(A and B) known.
- Read the headline answer and the table of related probabilities. The Venn diagram shows each region.
- Open the working to see each formula with your numbers filled in.
Features
- P(A and B), P(A or B), complements, conditional probabilities and exactly one or neither.
- Independent, mutually exclusive and known-overlap cases, with a check that the numbers are possible.
- Conditional probability with an independence check.
- Bayes' theorem with the total probability P(B) and a count table out of 10,000 people.
- Repeated trials: none, at least one, exactly k, at most k and at least k, using the binomial distribution.
- Venn diagram in SVG that scales to your screen.
- Decimals, percentages and fractions accepted everywhere.
At least one in n trials
The opposite of at least one is none, which is easy to calculate.
P(at least one) = 1 - (1 - p)^nWorked examples
At least one six in 4 rolls gives 0.517747
1 - (5/6)^4 = 1 - 0.482253.
At least one six in 10 rolls gives 0.838494
More trials make a success very likely, but never certain.
2% defect rate, a sample of 50 gives 0.63583
Chance of at least one defective item: 1 - 0.98^50 = 0.63583.
Privacy: how it works
- All calculations run in your browser tab. The probabilities you enter are not sent to Ulkaa or to any other server.
Tips
- Probabilities must be between 0 and 1. The calculator says which input is out of range.
- For "at least one", it is easier to find the chance of none and subtract from 1.
- If the overlap you enter is impossible for the given P(A) and P(B), the tool shows the allowed range.
- Repeated trials assume each trial is independent with the same chance.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your probabilities are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your probabilities are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
Why subtract from 1?
"At least one" covers every outcome except none, so its probability is 1 minus the chance of none.
Do the trials need to be independent?
Yes. The formula assumes each trial has the same chance and does not affect the others.
More Probability Calculator pages
- Probability CalculatorWork out the chance of two events together, either, or one given the other, with the steps and a Venn diagram.
- Conditional Probability CalculatorEnter P(A), P(B) and P(A and B) to get P(A given B) and P(B given A).
- Bayes' Theorem CalculatorEnter a prior, a sensitivity and a false positive rate to get the updated probability.