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 customer ordering a new car must choose a colour, an engine and a design of wheel.

There are $8$ colours and $3$ engines to choose from.

The customer can order the car in $120$ different ways.

Work out how many designs of wheel there are to choose from.

(2 marks)
Level 4 · 2 marksTry it
2
A school has a football team of $16$ players and a hockey team of $13$ players.

The school chooses a captain and a vice-captain from the players in each team.

Work out the number of different ways the four positions can be filled.

(3 marks)
Level 4 · 3 marksTry it
3
A security code is made from one letter chosen from A, B, C, D, followed by two digits, each chosen from $0$ to $9$ .

For example, C07 is a possible code.

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

(b) Work out how many of these codes have two digits that are different from each other.

(c) One of the codes from part (a) is chosen at random. Find the probability that it ends in $00$ .
Level 4 · 6 marksTry it
4
A club has six members: Ana, Ben, Cal, Dee, Eve and Femi.

(a) Two of the six members are chosen to go to a conference together. Work out how many different pairs could be chosen.

(b) Instead, one of the six is chosen as chairperson and a different one is chosen as secretary. Work out how many different ways this can be done.

(c) Explain how the answer to part (b) is related to the answer to part (a).
Level 4 · 4 marksTry it
5
A fair six-sided die numbered $1$ to $6$ is rolled, and a fair four-sided spinner numbered $1$ , $2$ , $3$ and $5$ is spun.

The number on the die is multiplied by the number on the spinner to give the score.

(a) Work out how many equally likely outcomes there are.

(b) Find the probability that the score is an odd number.

(c) Find the probability that the score is greater than $20$ .
Level 4 · 5 marksTry it