Several small chance-experiment trays with matching and contrasting tokens. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Write the repeated event in words first
If a single trial succeeds with probability p, n independent constant-probability trials all succeed with probability pⁿ. The chance of at least one success is instead 1−(1−p)ⁿ. These formulas describe different events, even though both start from the same one-trial odds.
Use a three-trial example
Odds in favor 1:4 correspond to p = 20%. Across three independent trials, all succeed with probability 0.2³ = 0.008, or 0.8%. At least one succeeds with probability 1−0.8³ = 0.488, or 48.8%. Adding 20% three times would give 60% and count outcomes with multiple successes more than once.
Check the independence assumption
A shared environmental factor, selection without replacement or changing difficulty can make the trials dependent or change p. Then the simple powers may not apply. For dependent all-success events, use a sequence of appropriate conditional probabilities. Observing past failures does not increase the next success probability under the independent fixed-p model.
Choose the appropriate level of detail
The Odds Calculator provides the two boundary event calculations for repeated chances. For exactly k successes or a cumulative success count, the binomial probability tool can represent a generic fixed-probability success trial, with heads interpreted as success. For adjacent runs, use the streak tool instead. Read the odds-direction guide before entering weights; confusing odds 1:4 with probability 1/4 changes every repeated-event result. A probability is a model statement, not a requirement that each small batch match its long-run percentage.
Check the model behind your result
Use the Odds Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26