Calculate probability from favourable outcomes and total outcomes, then show odds, complement probability, repeated-trial chance and a printable classroom or risk-note record.
Probability = favourable outcomes ÷ total outcomes. Percent probability = probability × 100. Complement = 1 − probability. Odds in favour = favourable outcomes : non-favourable outcomes. At least one success in n independent trials = 1 − (1 − probability)^n.
If 3 outcomes are favourable out of 10 total outcomes, probability = 3 ÷ 10 = 0.30 = 30%. The complement is 70%. The odds in favour are 3:7. Across 5 independent trials, the chance of at least one success is 1 − 0.70^5 = 83.193%.
Master’s Tip: write down what counts as an outcome before calculating. Most probability mistakes are not division mistakes; they come from counting the sample space inconsistently or treating dependent events as independent.
Standard or basis: elementary probability for finite outcome sets. Counts must describe one clearly defined trial. Repeated-trial output uses the standard independent-trial complement rule and should not be used when attempts affect each other.
Chance proof
Simple probability begins as favourable outcomes divided by total outcomes. The repeated-trial result uses the complement rule: calculate the chance of no success across independent trials, then subtract from one.
Visible checks
Methodology & Accuracy
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Probability = favourable outcomes ÷ total outcomes. Percent probability = probability × 100. Complement = 1 − probability. Odds in favour = favourable outcomes : non-favourable outcomes. At least one success in n independent trials = 1 − (1 − probability)^n.
Standard or basis: elementary probability for finite outcome sets. Counts must describe one clearly defined trial. Repeated-trial output uses the standard independent-trial complement rule and should not be used when attempts affect each other.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master’s Tip: write down what counts as an outcome before calculating. Most probability mistakes are not division mistakes; they come from counting the sample space inconsistently or treating dependent events as independent.
Divide the number of favourable outcomes by the total number of possible outcomes. Multiply by 100 if you want the answer as a percentage.
The probability is 3 ÷ 10 = 0.30, which is 30%. The complement, or chance of not getting that outcome on one trial, is 70%.
Complement probability is the chance that the event does not happen. It equals 1 minus the event probability, or 100% minus the event percentage.
Use it only when each trial is independent and has the same probability. A draw with replacement can fit that model; a draw without replacement usually does not.
Print the favourable outcomes, total outcomes, probability, complement, odds, repeated-trial assumption, formula and notes about what was counted. That makes the worksheet or risk note checkable later.
Probability is a compact way to describe uncertainty, but it only becomes trustworthy when the event and sample space are named clearly. A clean probability record states the counted favourable outcomes, the total outcome set, the complement and whether repeated attempts are independent.
Writing probability as favourable outcomes over total outcomes keeps the counting step visible. The decimal and percent forms are communication formats built from that fraction.
For independent repeated trials, it is often easier to calculate the chance of no success and subtract from one. That is why at-least-one probability uses 1 − (1 − p)^n.
Classroom, games, sampling and quality checks are easier to audit when the sample space, event definition, independence assumption and formula are printed beside the answer.