GCSE · Basic probability

Sample space & systematic listingExam-style questions

How to list every outcome once and only once — systematic listing, two-way sample-space diagrams, the product rule for counting, and why swapping two things over sometimes makes a new outcome and sometimes doesn't.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A coin is flipped and a fair four-sided dice (numbered $1$ to $4$ ) is rolled. List all the possible outcomes.
Level 1 · 1 markTry it
2
Two fair coins are flipped. Write down the probability of getting two heads.
Level 1 · 2 marksTry it
3
A menu has $3$ starters and $4$ main courses. How many different combinations of one starter and one main are there?
Level 1 · 1 markTry it
4
Spinner A has four equal sections numbered $1, 2, 3, 4$ . Spinner B has three equal sections numbered $1, 2, 3$ .

Both spinners are spun and the scores are added.

Work out the probability that the total is $5$ . [3]
Level 2 · 3 marksTry it
5
A fair coin is flipped and a fair four-sided spinner numbered $1$ , $2$ , $3$ , $4$ is spun.

(a) List all the possible outcomes.

(b) Find the probability of getting a head and an even number.
Level 2 · 4 marksTry it

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