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 four-digit code is made using these rules:
- the first digit must be odd,
- the last digit must be $0$ or $5$ ,
- the second and third digits can be any digit from $0$ to $9$ .
Digits may be repeated.

(a) Work out how many different codes are possible.

(b) A code is chosen at random from all the possible codes. Find the probability that all four of its digits are the same.
Level 5 · 5 marksTry it
2
In a football league every team plays every other team exactly once. Altogether $45$ matches are played.

(a) Work out how many teams are in the league.

(b) One of the $45$ matches is chosen at random. Rovers is one of the teams in the league.

Find the probability that the chosen match is one that Rovers plays in.
Level 5 · 5 marksTry it