Robinson Tuition
Grade 3 · Foundation · free GCSE maths worksheet

Sample space diagrams

Listing all outcomes of two events.

12 original questions, 30 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Ola is choosing an outfit.

She has 3 shirts: red (R), blue (B) and green (G).

She has 2 pairs of shorts: black (K) and white (W).

List all the possible outfits Ola can choose. One outfit, RK, has been done for you.

2 marks
Show answer
RK, RW, BK, BW, GK, GW
2

A cafe sells 3 hot drinks: tea (T), coffee (C) and hot chocolate (H).

It sells 2 cakes: flapjack (F) and brownie (B).

Noah chooses one hot drink and one cake.

List all the possible combinations Noah can choose.

2 marks
Show answer
TF, TB, CF, CB, HF, HB
3

Bag A contains three cards numbered 1, 2 and 3.

Bag B contains two cards numbered 5 and 7.

Erin takes one card from bag A and one card from bag B.

Write down all the possible pairs of cards Erin can take.

2 marks
Show answer
(1, 5), (1, 7), (2, 5), (2, 7), (3, 5), (3, 7)
4

Ali throws a fair coin 3 times.

Each throw lands on heads (H) or tails (T).

List all the possible outcomes of the 3 throws. One outcome, HHH, has been done for you.

2 marks
Show answer
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
5

A locker code is a letter followed by a prime number.

The letter is chosen from P, Q and R.

The prime number is chosen from 3 and 7.

List all the possible locker codes.

2 marks
Show answer
P3, P7, Q3, Q7, R3, R7
6

A pizza shop offers 4 toppings: mushroom (M), pepper (P), olive (O) and sweetcorn (S).

Jo chooses 2 different toppings for her pizza.

List all the possible pairs of toppings Jo can choose.

2 marks
Show answer
MP, MO, MS, PO, PS, OS
7

Spinner A has three equal sections numbered 1, 2 and 3.

Spinner B has two equal sections numbered 4 and 5.

Both spinners are spun and the two numbers are multiplied together.

List all the possible products.

2 marks
Show answer
4, 5, 8, 10, 12, 15
8

Ivy has three coins: a 5p coin, a 10p coin and a 20p coin.

She picks two different coins and adds their values.

List all the possible totals.

2 marks
Show answer
15p, 25p, 30p
9

Spinner A has sections numbered 1, 2 and 3. Spinner B has sections numbered 1 and 2.

Both spinners are spun and the two scores are added together. Part of the sample space table is shown.

Spinner B \ Spinner A123
1234
2   
  1. Complete the table.
  2. Write down the probability that the total score is 4.
3 marks
Show answer
a) 3, 4, 5 b) 1/3
10

A fair coin is thrown and a fair four-sided spinner, numbered 1, 2, 3 and 4, is spun.

  1. List all the possible outcomes. One has been done for you: H1.
  2. Work out the probability of getting a head and an even number.
3 marks
Show answer
a) H1, H2, H3, H4, T1, T2, T3, T4 b) 1/4
11

Mia picks a card at random from cards numbered 1, 2 and 3.

Kofi picks a card at random from cards numbered 2 and 4.

Their two numbers are added together.

  1. Draw a sample space table to show all the possible totals.
  2. Work out the probability that the total is an odd number.
4 marks
Show answer
a) 1+2=3, 1+4=5, 2+2=4, 2+4=6, 3+2=5, 3+4=7 b) 2/3
12

Two fair six-sided dice are rolled and their scores are added together.

  1. Draw a sample space diagram to show all the possible total scores. How many outcomes are there?
  2. Work out the probability that the total is 7.
  3. Work out the probability that the total is at least 9.
4 marks
Show answer
a) 36 outcomes b) 1/6 c) 5/18

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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