The Probability Scale from 0 to 1

How likely is it?

Every day you guess how likely things are. Will it rain? Will the bus be late? In maths we measure likelihood with probability, and we line it up on a special number line called the probability scale.

The 0 to 1 line

The scale starts at 0 and ends at 1.

• 0 means the event is impossible — it can never happen.
• 1 means the event is certain — it will definitely happen.
• The middle means an even chance — just as likely to happen as not.

0 ————————— 1/2 ————————— 1 impossible even chance certain

Nothing can be less than 0 or more than 1. If you ever work out a probability bigger than 1, something has gone wrong.

Words for likelihood

We can describe chance with everyday words. Here is how those words match the scale:

Word	Roughly where on the scale	Example
Impossible	0	Rolling a 7 on a normal die
Unlikely	near 0	Snow in summer
Even chance	1/2	A fair coin landing heads
Likely	near 1	A new battery still working tomorrow
Certain	1	Tomorrow has a daytime

Worked example: place the event

Where does rolling an even number on a six-sided die go on the scale?

1. List the numbers: 1, 2, 3, 4, 5, 6.
2. The even ones are 2, 4, 6 — that is 3 out of 6.
3. 3 out of 6 is the same as 1 out of 2, or 1/2.

So rolling an even number is an even chance. It sits right in the middle of the scale.

Worked example: certain or impossible?

A bag holds only red counters.

• Picking a red counter is certain — every counter is red, so it sits at 1.
• Picking a green counter is impossible — there are no green ones, so it sits at 0.

Activity: build your own scale

Draw a long line and label 0 at one end, 1 at the other, and 1/2 in the middle. Then write each of these events in the right place:

1. The day after Monday is Tuesday.
2. A dropped coin lands on tails.
3. A cat lays an egg.
4. It will rain at some point this month.

Talk about why you chose each spot. There is no single perfect answer for the "likely" and "unlikely" ones, and that is fine — the point is to compare them sensibly.

Why this matters

The probability scale gives us a fair, shared way to talk about chance instead of vague guessing. Once you are comfortable placing events from 0 to 1, you are ready to calculate exact probabilities by counting outcomes. Build on this with probability basics, and strengthen the fractions behind it with introduction to fractions.