Reason with probability

Count the possible outcomes and choose the exact answer.

Coins, dice sums and at least one

Eight questions. No time limit.

What can happen?

Read what is random and what is being counted. Choose the exact probability or expected point value.

Two fair dice: 36 equally likely ordered outcomes.

How to play

Choose one of four answers. The answer locks when selected. Read the method, then choose Next question.

Count equally likely outcomes, not just different-looking results. Two dice have 36 ordered outcomes, but their sums are not equally likely.

All answers are exact. Fractions may represent probabilities or point values. For draws without replacement, the bag changes after the first draw.

Expected payout is the average points received over many repetitions, not a promised result on one roll. Expected net gain subtracts the fixed cost and can be negative.

Finish all eight questions to save a result in this browser. An unfinished round is not saved. Active time includes answers and review, but not background tabs. There is no time limit or speed bonus.

Use Tab and Enter or Space to choose an answer. Keys 1–4 also select answers, except when another control is focused.

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