Chance: Impossible to Certain

What you will learn

• Use the words impossible, unlikely, even chance, likely and certain.
• Place events on a chance line.
• Compare chances by counting outcomes.

Before you start: you should be able to compare numbers and know halves and quarters. See Fractions.

The idea

Some things will definitely happen, some cannot happen and many are somewhere in between. We use words to say how likely an event is. Together they make a scale called the chance line.

Using the words

• Impossible: it can never happen, such as rolling a $7$ on a normal die.
• Unlikely: it could happen, but probably will not.
• Even chance: it is as likely to happen as not, such as getting heads.
• Likely: it will probably happen.
• Certain: it will definitely happen.

Counting outcomes

To compare chances, count how many outcomes there are in total and how many are the ones you want. A bag with $3$ red and $1$ blue counter is more likely to give red than blue.

Worked examples

Example 1: Choosing the word

You roll a normal die. How likely is an even number?

1. Even numbers: $2, 4, 6$, so $3$ out of $6$.
2. Half the outcomes are even.

Answer: even chance

Example 2: Comparing

A bag has $5$ yellow and $2$ green counters. Which colour is more likely?

1. Yellow $5$, green $2$.
2. There are more yellow counters.

Answer: yellow is more likely

Example 3: Making a spinner

Make a spinner where blue is unlikely and red is likely. Use $4$ equal sections.

1. Red must have more sections than blue.
2. Use $3$ red and $1$ blue.

Answer: red $3$, blue $1$

Tip: an event with no chance is impossible and an event that always happens is certain. Everything else sits between.

Why it matters

We use chance words every day: weather forecasts, games and everyday decisions. Next, probability turns these words into numbers from $0$ to $1$.