DIY Cost Tools
Probability Calculator
MATH CALCULATOR
Calculate single-event probability, expected successes, and the chance of at least one success across repeated independent trials.
How it works
For equally likely outcomes, divide favorable outcomes by total outcomes. For repeated independent trials, the complement rule finds the chance of one or more successes.
Formula
p = favorable ÷ total. P(at least one in n trials) = 1 − (1 − p)n. Expected successes = n × p.
Worked example
With 3 favorable outcomes among 10 and five independent trials, p is 30%, the probability of at least one success is about 83.193%, and the expected number is 1.5.
Important limits
- Outcomes must be equally likely for favorable divided by total to apply directly.
- Repeated-trial results assume independence and the same probability on every trial.
- Expected value is a long-run average, not a guarantee for one set of trials.
Frequently asked questions
Why use the complement rule?
It is often simpler to calculate the chance of no successes and subtract it from one.
Can expected successes be a decimal?
Yes. It describes a long-run average across many repetitions.
Sources and review notes
The tool applies basic probability definitions, the complement rule, and the expected value of a binomial setting. Last reviewed September 29, 2026.