Year 8 · Maths · Tables and probability · Lesson 1

Sample spaces and probability

Learn to list outcomes systematically, draw sample space diagrams for two dice or spinners, find probabilities, use P(not) = 1 − P, and work out expected outcomes.

32-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

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What your child will learn

List all outcomes of two events systematically
Draw and use a sample space diagram
Find probabilities as fractions
Use the fact that P(not A) = 1 − P(A)
Work out expected outcomes

The method

Draw a grid with one event down the side and one across the top.
Fill in every outcome.
Count the outcomes you want.
Probability = wanted ÷ total; simplify.

Key words: probability, outcome, sample space, equally likely, expected.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

A coin is thrown twice. List all the possible outcomes.

Step 1: Go through every first throw with every second throw.
Step 2: HH, HT
Step 3: TH, TT
Step 4: 2 × 2 = 4 outcomes

Answer: 4 outcomes

Question 2

A spinner with A, B, C is spun and a coin is thrown. List all the possible outcomes.

Step 1: Go through every letter with every coin result.
Step 2: AH, AT
Step 3: BH, BT
Step 4: CH, CT
Step 5: 3 × 2 = 6 outcomes

Answer: 6 outcomes

Question 3

Two dice are rolled and the scores added. Find the probability of a total of 7.

Step 1: Draw the sample space diagram
Step 2: Total outcomes: 6 × 6 = 36
Step 3: Total 7: 6 outcomes
Step 4: P = 6/36
Step 5: 6/36 = 1/6 (÷ 6)

Answer: 1/6