Maths topic

chance

Chance describes how likely something is to happen. We can use chance words, list outcomes, compare events and record trials.

Practise chance Explore probability Back to topics

the big idea

Chance is about possible results. If we know the outcomes, we can describe how likely an event is and compare it with another event.

event roll a die
outcome roll a 3
chance 1 out of 6
trials record what happens

compare chance models

Choose a model and read the possible outcomes, chance word and simple probability.

roll a 3 unlikely 1/6
1 2 3 4 5 6

Die: unlikely

eventroll a 3 outcomes6 possible outcomes probability1/6 rememberRolling a 3 is 1 of 6 equally likely outcomes.
model

chance words describe likelihood

Chance words help us describe how likely something is to happen.

  • Impossible means it cannot happen.
  • Unlikely means it could happen, but probably will not.
  • Even chance means it is just as likely to happen as not happen.
  • Likely means it will probably happen.
  • Certain means it will happen.
impossible 0/6
unlikely 1/6
even chance 3/6
likely 5/6
certain 6/6

outcomes are possible results

An outcome is one possible result of an event.

  • An event is the action, such as rolling a die.
  • An outcome is one result, such as rolling a 3.
  • Listing all possible outcomes helps us judge chance.
event roll a die
1 2 3 4 5 6

Rolling a 3 is one possible outcome.

fair events have equally likely outcomes

In a fair event, each outcome has the same chance of happening.

  • A fair coin has 2 equally likely outcomes: heads and tails.
  • A fair six-sided die has 6 equally likely outcomes: 1, 2, 3, 4, 5 and 6.
  • Equally likely outcomes have the same chance.
flip heads even chance 1/2
heads tails
2 equally likely outcomes
roll a 3 unlikely 1/6
1 2 3 4 5 6
6 equally likely outcomes

probability can be written as a fraction

Probability is a number that describes chance. It can be written as favourable outcomes out of total possible outcomes.

  • A favourable outcome is the outcome we are looking for.
  • The denominator tells how many possible outcomes there are.
  • Rolling a 3 on a fair six-sided die has probability 1/6.
roll a 3 unlikely 1/6
1 2 3 4 5 6
favourable 1 out of 6 possible

compare chance by counting favourable outcomes

If one event has more favourable outcomes, it has a greater chance.

  • A spinner with more yellow sections is more likely to land on yellow.
  • A bag with more blue counters is more likely to give a blue counter.
  • Count favourable outcomes and total outcomes before comparing.
2/4 yellow
pick blue likely 3/5
blue blue blue red red
3/5 blue

More favourable outcomes gives a greater chance.

trials record what actually happened

A trial is one go at a chance experiment. We can tally trial results to see what happened.

  • One coin flip is one trial.
  • Trials record results that happened, not just what could happen.
  • More trials can make patterns easier to see.
12 coin flip trials
resulttallycount
heads 7
tails 5

The tally shows what actually happened.

chance words

These words help us talk about possible results and how likely they are.

1 chance likelihood

how likely something is to happen

2 event action

the chance action, such as rolling a die

3 outcome result

one possible result of an event

4 probability number

a number that describes chance

5 favourable outcome wanted result

an outcome we are looking for

6 trial one go

one go at a chance experiment

7 fair same chance

each outcome is equally likely

chance facts

fact Impossible means cannot happen
fact Certain means will happen
fact A fair coin has 2 equally likely outcomes
fact A fair six-sided die has 6 outcomes
fact Rolling a 3 on a fair die has probability 1/6
fact More favourable outcomes means a greater chance

real world examples

games rolling dice and spinning spinners
weather talking about the chance of rain
sport predicting possible match outcomes
surveys choosing a student name at random
science running repeated trials in an experiment
data tallying results from coin flips or dice rolls

quick chance quiz

Try a few chance ideas. This quiz only asks about ideas shown on this page.

Which event is impossible on a normal six-sided die?

How many possible outcomes are on a fair six-sided die?

What is the probability of rolling a 3 on a fair six-sided die?

A bag has 3 blue counters and 2 red counters. Which colour is more likely?

What does a trial record?