Probability Question Generator

Builds a sheet of probability questions from counters in a bag, at the level you ask for. Every answer is a fraction in its lowest terms, computed from the counts rather than estimated. Every question is computed and checked directly — not a fabricated or AI-guessed fact.

How many questions

Between 1 and 30. The sheet below shows how many pages they take.

Level

Seed (optional)

A word reproduces the same sheet, so a whole class can be given the identical set.

Gentle is a single event and its complement. Standard adds either-or; stretch adds two draws, with and without replacement.

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

Room to answer in

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. The page addresses and dates a browser normally prints across the top and bottom are already kept off.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

Your questions will appear here.

What this generator does

Generates probability questions with answers — single events, combined events and complements. Answers are given as fractions in their lowest terms, which is the form these questions are usually marked in.

How to use this tool

Choose a level and how many questions you want.
Press make questions and work through the sheet.
Show the answers to mark it, or show the working to see how the favourable outcomes were counted.
Enter a seed word to rebuild the same sheet later.

Worked examples

A complement, gentle level, seed round9: A bag holds 2 red and 4 blue counters; the probability that one taken at random is NOT red → 2/3, since 4 of the 6 are not red.

Common use cases

Probability practice at home or school
Quick maths warm-ups
Self-testing before a maths quiz

How this generator works

A bag composition is drawn first, then the question type — a single draw, a complement, an either-or, or a second draw with or without replacement. The probability is computed exactly as a fraction of counts rather than estimated, and is reduced to lowest terms by dividing through by the highest common factor of numerator and denominator before it is shown.

Randomness and fairness

The scenario and its numbers are drawn with the browser's cryptographic random number generator. The probability in each answer is computed exactly rather than estimated, so a question about drawing from a bag reports the true fraction rather than a simulated frequency. A seed word rebuilds the same sheet later for as long as the generator is unchanged; a seed is for reproducibility, not cryptographic strength, so a seeded sheet is deterministic rather than unpredictable.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

The scenario is always counters in a bag. Dice, cards and spinners are not modelled, though the underlying fraction arithmetic is the same.
With replacement and without replacement are both offered, but only for two draws — a chain of three or more draws is not produced.
Probabilities are shown as fractions only; a question requiring the answer as a decimal or a percentage is not set here.

Common mistakes

Adding probabilities that should be multiplied: Independent events happening together multiply. Mutually exclusive alternatives add. Deciding which situation you have is the whole question.
Forgetting that removing an item changes the next probability: Drawing without replacement changes both the numerator and the denominator for the second draw.