GCSE MATHS • HIGHER TIER

Basic Probability Made Simple

Understand chance, identify outcomes and calculate probabilities confidently.

Clear method

Exam practice

Worked proofs

Basic Probability in Four Moves

1 Identify

Identify the event and the possible outcomes.

2 Count

Count the favourable outcomes and the total possible outcomes.

3 Calculate

Use the probability formula and simplify when needed.

4 Interpret

Check that the probability lies between 0 and 1 and makes sense.

What You’ll Learn

Understand what probability measures.

Use the probability scale from 0 to 1.

Apply the basic probability formula.

Calculate probabilities from dice, coins, bags, spinners and cards.

Write probabilities as fractions, decimals and percentages.

Interpret probability in real-life situations.

Key Rules

Probability measures how likely an event is to happen.

Use the formula :

Probability = Favourable outcomes ÷ Total possible outcomes.

Probabilities must be between 0 and 1.

A probability of 0 means impossible.

Worked Proof: Basic Probability

Step-by-Step Method

1. Identify the event you are finding the probability of.
2. Count the number of favourable outcomes.
3. Count the total number of possible outcomes.
4. Divide the favourable outcomes by the total outcomes.
5. Simplify the fraction if possible.

More Worked Examples

1

Question: What is the probability of rolling a 3 on a fair six-sided dice?

Step 1: Count favourable outcomes .

Only one outcome gives a 3 .
Step 2: Count total outcomes.
There are 6 possible outcomes.
Probability = 1/6

Answer: 1/6

2

Question: What is the probability of tossing a fair coin and getting heads?

Favourable outcomes = 1

Total outcomes = 2
Probability = 1/2

Answer: 1/2

3

Question: A bag contains 5 red balls and 3 blue balls. What is the probability of selecting a red ball?

Total balls = 8

Red balls = 5
Probability = 5/8

Answer: 5/8

4

Question: A spinner has 8 equal sections. Three are green. Find the probability of landing on green.

Probability = 3/8

Answer: 3/8

Write down the favourable outcomes before calculating.
Count the total number of possible outcomes carefully.
Use the probability formula when outcomes are equally likely.
Simplify fraction answers where possible.
Remember that every probability must be between 0 and 1.
Convert between fractions, decimals and percentages when the question requires it.