Basic Probability (Years 6–9) — Maths

Will it rain tomorrow? Will a flipped coin land heads? Will you draw the red counter from the bag? Probability measures how likely something is, on a scale from 0 (impossible) to 1 (certain). A probability of 0.5 means "as likely as not" — like a fair coin landing heads.

Why this matters: probability is how weather forecasts, games, insurance and medical tests are described. Learning to turn "how likely?" into a number lets you compare risks sensibly and spot when a claim about chance does not add up.

Every probability sits somewhere from 0 to 1

The probability scale

Every probability lands somewhere on the 0-to-1 line. It never goes below 0 or above 1 — if you ever calculate a chance of 1.3 or −0.2, you have made a mistake. Words map onto the scale like this:

Value	Meaning	Example
0	Impossible	Rolling a 7 on an ordinary dice
0.25	Unlikely	Drawing a spade from a pack
0.5	Even chance	A fair coin landing heads
0.75	Likely	Not drawing a spade from a pack
1	Certain	Rolling a number below 7 on a dice

Working out a probability

When all the outcomes are equally likely, probability is just a fraction — a comparison of the outcomes you want against every outcome that could happen:

P(event) = (number of ways it can happen) ÷ (total number of outcomes)

A dice has 6 equally likely outcomes — so P(a 4) = 1 out of 6.

Rolling a 4 on a dice: 1 way to get a 4, out of 6 equally likely outcomes → P = 1/6.
Rolling an even number: 3 ways (2, 4, 6) out of 6 → 3/6 = 1/2.
A bag of 3 red and 2 blue counters: P(red) = 3 out of 5 = 3/5.

3 red out of 5 counters: P(red) = 3/5 — wanted outcomes over the total.

The "not" rule

The probabilities of every possible outcome always add up to 1 (something is certain to happen). So the chance of something not happening is simply 1 minus the chance it does — a shortcut that saves counting all the other outcomes:

P(not A) = 1 − P(A)

All outcomes fill the bar to 1, so P(not A) = 1 − P(A).

If P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7. If P(rolling a 6) = 1/6, then P(not a 6) = 1 − 1/6 = 5/6.

Common mistake: a probability can never be bigger than 1 or a "chance out of 6" written as a whole number. Answers must be a fraction, decimal or percentage between 0 and 1 — if you get 6/1 or 1.5, you have flipped the fraction or added when you should have subtracted.

In a nutshell: probability runs from 0 to 1; it is favourable outcomes ÷ total outcomes; and P(not happening) = 1 − P(happening).