DeepMaths Junior

Junior Maths Book 1 AI Learning System

For Years 7-9 - Numbers & Statistics

Chapter 8: Probability Basics

Probability Basics

Reason from possible outcomes instead of guessing from intuition.

Junior Maths Book 1 pages 143-1508 minutes

AI teacher

Start the short explanation, then use the visual model and practice before returning to the workbook.

Voice: Browser voice

Workbook pages

Junior Maths Book 1 pages 143-150

Use probability language, scales, sample spaces and simple combined events.

AI explanation

The AI teacher places events on a probability scale, builds sample spaces in tables and uses fractions to describe favourable outcomes out of all equally likely outcomes.

  1. 1Probability ranges from 0 to 1.
  2. 20 means impossible and 1 means certain.
  3. 3A sample space lists all possible outcomes.
  4. 4For equally likely outcomes, probability is favourable outcomes divided by total outcomes.

Animated teaching

See the method

A probability scale marks impossible to certain, then a two-way sample-space grid fills with possible outcomes.

Probability scale from impossible to certain00.250.50.751impossiblecertain
H,1
H,2
H,3
T,1
T,2
T,3

Why this method works

  • A probability fraction compares the event to the entire outcome space.
  • Sample spaces prevent missing or double-counting outcomes.
  • Combined events can be organised with tables or tree-style reasoning.

Common mistakes

  • Counting favourable outcomes but not total outcomes.
  • Assuming outcomes are equally likely when they are not.
  • Forgetting that probabilities cannot be greater than 1.
  • Missing outcomes in a sample space.

Multiple methods

  • Sample spaces can be listed, shown in a table or represented in a tree diagram.
  • Probabilities can be written as fractions, decimals or percentages.
  • Experimental probability can be compared with theoretical probability.

Worked examples

Sample space

A fair coin and a fair spinner labelled 1, 2, 3 are used. How many outcomes are possible?

Method: List pairs.

  1. 1.Coin outcomes: H, T.
  2. 2.Spinner outcomes: 1, 2, 3.
  3. 3.Each coin outcome pairs with each spinner outcome.
  4. 4.2 x 3 = 6.

Answer: 6 outcomes

Probability

A bag has 4 red, 3 blue and 5 green counters. Find P(green).

Method: Favourable outcomes over total outcomes.

  1. 1.There are 5 green counters.
  2. 2.Total counters = 4 + 3 + 5 = 12.
  3. 3.P(green) = 5/12.

Answer: 5/12

Interactive practice

Try before you look

0/3 correct, 0 answered

Question 1

Which probability means certain?

Question 2

A fair dice is rolled. What is P(rolling an even number)?

Question 3

Why is a sample space useful?

Review prompt

Explain why listing outcomes can change a probability answer.

Write a two-sentence answer in your notebook before marking the workbook section complete.

Challenge question

Two fair coins are tossed. A student says P(one head and one tail) is 1/3 because the results are two heads, two tails, or mixed. Explain the error.

Hint: List HH, HT, TH and TT.