Probability Calculator

Calculate probability from favourable outcomes and total outcomes, then show odds, complement probability, repeated-trial chance and a printable classroom or risk-note record.

Probability3 favourable ÷ 10 total · complement 70% · odds in favour 3:7 · at least one success in 5 independent trials: 83.193% · comparison 50%

Favourable outcomesTotal possible outcomesRepeated independent trialsComparison probability%

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Probability Calculator: 30%. 3 favourable ÷ 10 total · complement 70% · odds in favour 3:7 · at least one success in 5 independent trials: 83.193% · comparison 50%

Formula applied

The exact method behind this answer

CalculationTime keeps the method visible so the number can be checked instead of blindly 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.

Apply the formulaProbability = 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.30%3 favourable ÷ 10 total · complement 70% · odds in favour 3:7 · at least one success in 5 independent trials: 83.193% · comparison 50%

Your live breakdown

Current inputs in the calculation

These values come from the controls above and update when the calculator changes.

Favourable outcomes: 3
Total possible outcomes: 10
Repeated independent trials: 5
Comparison probability: 50 %

Resulting answer

30%

3 favourable ÷ 10 total · complement 70% · odds in favour 3:7 · at least one success in 5 independent trials: 83.193% · comparison 50%

Answer: 30%
Live support: 3 favourable ÷ 10 total · complement 70% · odds in favour 3:7 · at least one success in 5 independent trials: 83.193% · comparison 50%

Assumptions used

What this answer assumes

Best for classroom worksheets, chance comparisons, board-game notes, quality-control examples, sampling explanations and simple risk records where the counted outcomes and assumptions need to stay visible.

The favourable outcomes are part of the total outcome set for one trial.
The simple probability assumes outcomes are equally likely unless the user has already weighted the counts appropriately.
The repeated-trial line assumes independent trials with the same probability each time, such as replacement draws or repeated attempts under the same conditions.
This page is for transparent arithmetic and classroom or planning notes, not gambling advice, medical risk prediction or formal statistical modelling.

Master’s Tip

How to use the result well

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.

Printable record

What belongs in the saved calculation

Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.

Favourable outcomes: 3
Total possible outcomes: 10
Repeated independent trials: 5
Comparison probability: 50 %

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Formula

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.

Worked example

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%.

Professional note

Regional and unit assumptions

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

At least one success

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

What the page now proves

Favourable ÷ total
Complement probability
Independent repeated-trial warning

Assumptions and limitations

The favourable outcomes are part of the total outcome set for one trial.
The simple probability assumes outcomes are equally likely unless the user has already weighted the counts appropriately.
The repeated-trial line assumes independent trials with the same probability each time, such as replacement draws or repeated attempts under the same conditions.
This page is for transparent arithmetic and classroom or planning notes, not gambling advice, medical risk prediction or formal statistical modelling.

Methodology & Accuracy

How this calculator is checked

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.

Formula used

Standard or basis

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

Questions

How do I calculate probability?

Divide the number of favourable outcomes by the total number of possible outcomes. Multiply by 100 if you want the answer as a percentage.

What is the probability of 3 favourable outcomes out of 10?

The probability is 3 ÷ 10 = 0.30, which is 30%. The complement, or chance of not getting that outcome on one trial, is 70%.

What does complement probability mean?

Complement probability is the chance that the event does not happen. It equals 1 minus the event probability, or 100% minus the event percentage.

When can I use the repeated-trial result?

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.

What should I print for a probability record?

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.

Calculation note

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.

Probability is a fraction before it is a percent

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.

Complements simplify repeated attempts

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.

Printed probability notes prevent hidden assumptions

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.

Sources and further readingOpenStax Introductory Statistics — Probability Topics Khan Academy — Basic probability