Probability: measuring chance

Will it rain? Will this coin land heads? Probability is the branch of maths that measures how likely something is, turning vague words like 'probably' into precise numbers. It runs through games, weather, insurance, medicine and science. This lesson shows how to measure chance and reason about it clearly.

Chance as a number from 0 to 1

The probability of an event is a number between 0 and 1 that says how likely it is. 0 means impossible, 1 means certain, and 0.5 (a half) means equally likely to happen or not. Probabilities are often written as fractions, decimals, or percentages — 1/2, 0.5, and 50% all mean the same chance.

For events where every outcome is equally likely, the probability is simply: the number of ways it can happen, divided by the total number of possible outcomes.

Counting outcomes

Take rolling a fair six-sided die. There are 6 equally likely outcomes (1 to 6). The chance of rolling a 3 is one favourable outcome out of six: 1/6. The chance of rolling an even number (2, 4 or 6) is three out of six, which is 3/6 = 1/2.

So the recipe is: count the outcomes you want, count all the outcomes, and make a fraction. The picture below shows the 1-in-6 chance of a single number on a die.

One outcome out of six equally likely ones: the probability is 1/6.

Worked example

What is the probability of rolling an even number on a six-sided die?

Favourable outcomes (even): 2, 4, 6 — that's 3.
Total outcomes: 1, 2, 3, 4, 5, 6 — that's 6.
Probability = favourable ÷ total = 3/6.

Answer: 3/6 = 1/2 (a 50% chance)

Certain, impossible, and the complement

Some events are certain (probability 1), like rolling a number from 1 to 6. Some are impossible (probability 0), like rolling a 7. Everything else sits in between.

A handy rule: the chance an event does not happen is 1 minus the chance it does. If the chance of rain is 0.3, the chance of no rain is 1 − 0.3 = 0.7. This 'complement' trick often saves work — sometimes it's easier to find the chance of the opposite and subtract.

Check yourself

Try these. Pick an answer to see whether it's right and why.

A probability of 0 means the event is:

0 means it cannot happen; 1 means it is certain; 0.5 means equally likely.

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

One favourable outcome (3) out of six equally likely outcomes: 1/6.

What is the probability of rolling an even number on a six-sided die?

Even outcomes are 2, 4, 6 — three out of six, which is 3/6 = 1/2.

If the chance of rain is 0.3, what is the chance of no rain?

The complement is 1 − 0.3 = 0.7.

Rolling a 7 on a normal six-sided die has probability:

There is no 7 on the die, so it is impossible — probability 0.

In a nutshell

Probability measures chance as a number from 0 (impossible) to 1 (certain); 0.5 is equally likely.
For equally likely outcomes, probability = favourable outcomes ÷ total outcomes.
Certain events have probability 1, impossible events 0.
The chance an event does NOT happen is 1 minus the chance it does.

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