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Study GuideYear 6Level 1 · Easier

Free Year 6 Probability Basics

Introduces the probability scale from 0 to 1, how to calculate the chance of an event when outcomes are equally likely, how to write probabilities as fractions, decimals and percentages, and how to predict expected results. Uses dice, marbles and spinners, with worked examples and a self-check.

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Year
Year 6
Subject
Mathematics
Topic
Probability
Difficulty
Level 1 · Easier
Estimated time
15 minutes
Curriculum
Australian Curriculum
Answers
Not applicable
Format
PDF (A4) + print

Students will practise

  • understanding the probability scale from impossible (0) to certain (1)
  • calculating probabilities for equally likely outcomes
  • understanding complementary events (the chance that something does not happen)
  • predicting expected results from a probability

Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Probability Basics

  1. 1Year 6 Probability Worksheet — Level 2
Study guide

How to use this study guide

  1. Read it together first, pausing at each worked example to try the step before reading the answer.
  2. Attempt the "Check yourself" questions at the end without looking back.
  3. Then practise with a worksheet from the pathway above and finish with the topic test.

Common questions

Who is this study guide for?

Year 6 students (typically ages 11–12) working on probability. It is pitched at level 1 · easier.

Are the answers included?

This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.

How long does it take?

About 15 minutes. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Try Year 6 Probability Worksheet — Level 2.

Preview

Year 6 · Mathematics · Probability

Probability Basics

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What you need to know

Probability measures how likely something is to happen. It is always a number between 0 (impossible) and 1 (certain). You can write it as a fraction, a decimal or a percentage: an even chance is = 0.5 = 50%.

When every outcome is equally likely, use the rule: probability = number of favourable outcomes ÷ total number of outcomes. A favourable outcome is one that counts as the event you are interested in.

WordProbability
Impossible0
Unlikelybetween 0 and
Even chance (0.5 or 50%)
Likelybetween and 1
Certain1

Rolling a standard six-sided die

  1. There are 6 equally likely outcomes: 1, 2, 3, 4, 5, 6.
  2. P(rolling a 4) = , because only one outcome is a 4.
  3. P(rolling an even number) = = , because 2, 4 and 6 are even.
  4. P(rolling a number less than 3) = = , because 1 and 2 count.
  5. P(rolling a 7) = 0. It is impossible.

A bag holds 3 red, 5 blue and 2 green marbles. One is picked without looking.

  1. Total marbles: 3 + 5 + 2 = 10.
  2. P(blue) = = = 0.5 = 50%.
  3. P(red or green) = + = = .
  4. P(not red) = = 0.7 = 70%, because 7 of the 10 marbles are not red.

A spinner has red, blue and yellow sections. P(red) = 0.3 and P(blue) = 0.45. Find P(yellow).

  1. The probabilities of all the possible outcomes add up to 1.
  2. P(yellow) = 1 − 0.3 − 0.45 = 0.25.
  3. Check: 0.3 + 0.45 + 0.25 = 1.
  4. The same idea gives the chance that something does not happen: P(not red) = 1 − 0.3 = 0.7.

Expected results. If you repeat an experiment many times, the number of times you expect an event is probability × number of trials. Flip a coin 50 times and you expect about 25 heads. The real result might be 22 or 28; that is normal. Results from an actual experiment are called experimental probability, while the calculated value is theoretical probability. The more trials you do, the closer they usually get.

A die is rolled 60 times. How many sixes would you expect?

  1. P(six) = .
  2. Expected number of sixes = × 60 = 60 ÷ 6 = 10.
  3. If you actually rolled 8 sixes, that is not wrong; it is normal variation.
Common mistake: thinking a result is "due". If a coin lands on heads four times in a row, the chance of heads on the next flip is still . The coin has no memory.
Common mistake: counting outcomes without checking they are equally likely. A footy game has two outcomes, win or lose, but that does not make the chance of winning . The formula only works when every outcome has the same chance, like the faces of a fair die.

Check yourself

  1. What is the probability of rolling a 5 on a standard die?
  2. What is the probability of rolling an odd number on a standard die?
  3. A bag holds 4 red and 6 yellow lollies. Write P(yellow) as a fraction, a decimal and a percentage.
  4. The chance of rain tomorrow is 0.35. What is the chance it does not rain?
  5. A card is drawn from a standard pack of 52 playing cards. What is P(heart)?
  6. A spinner with 4 equal sections numbered 1 to 4 is spun 80 times. How many times would you expect a 3?

Answers: 1. 2. = 3. = , 0.6, 60% 4. 0.65 5. = 6. 20 (because × 80 = 20)

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More Year 6 probability resources

  • Worksheet

    Year 6 Probability Worksheet — Level 2

    Simple probability with marbles, spinners, dice and cards, written as fractions. Expected-level practice for this year group. This Year 6…

    Difficulty
    Level 2 · Standard
    Time
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    Questions
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    Answers
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About this resource

Created by
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Last reviewed
1 October 2026
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