GCSE Maths grade 4 basics · topic 7 of 9

Basic probability: GCSE Maths grade 4 basics

Probability measures how likely something is, from 0 (impossible) to 1 (certain). Most basic questions need just one fraction: the outcomes you want over all the outcomes.

Practise: 10 questions Read the basics first

In plain English

Probability = number of outcomes you want ÷ total number of equally likely outcomes. Write it as a fraction, decimal or percentage, never as "1 in 4" or a ratio.
All the probabilities for one event add up to 1, so P(not A) = 1 − P(A).
Expected number of times = probability × number of trials.
Two events (two coins, two dice): list every outcome, or draw a sample-space grid, then count.

Worked example

A bag has 4 red and 6 blue counters. One is taken at random. Find the probability it is red.

Total counters: 4 + 6 = 10
Red counters: 4
P(red) = 4/10 = 2/5

Answer: 2/5

Most common mistake

Wrong4 red and 6 blue counters: P(red) = 4/6

RightP(red) = 4/10 = 2/5

The bottom of the fraction is the total number of counters (4 + 6), not the number of the other colour.

Practice questions (10)

Try each one on paper first, then open the worked answer and mark yourself. You don't need a calculator for any of these.

Q1.A fair six-sided dice is rolled. Find the probability of rolling a 5.
Show worked answer
1. One outcome is a 5; there are 6 equally likely outcomes
2. P(5) = 1/6
Answer: 1/6
Q2.A fair six-sided dice is rolled. Find the probability of rolling an even number.
Show worked answer
1. Even numbers: 2, 4, 6, which is 3 outcomes
2. P(even) = 3/6 = 1/2
Answer: 1/2
Q3.A bag has 3 red, 5 blue and 2 green beads. One bead is picked at random. Find P(blue).
Show worked answer
1. Total: 3 + 5 + 2 = 10
2. P(blue) = 5/10 = 1/2
Answer: 1/2
Q4.Using the same bag (3 red, 5 blue, 2 green), find the probability the bead is not red.
Show worked answer
1. P(red) = 3/10
2. P(not red) = 1 − 3/10 = 7/10
Answer: 7/10
Q5.The probability that it rains tomorrow is 0.3. What is the probability that it does not rain?
Show worked answer
1. P(not rain) = 1 − 0.3
2. = 0.7
Answer: 0.7
Q6.A spinner can land on A, B, C or D. P(A) = 0.2, P(B) = 0.35 and P(C) = 0.15. Find P(D).
Show worked answer
1. The probabilities add up to 1
2. 0.2 + 0.35 + 0.15 = 0.7
3. P(D) = 1 − 0.7 = 0.3
Answer: 0.3
Q7.The probability a spinner lands on red is 0.4. It is spun 50 times. How many times would you expect it to land on red?
Show worked answer
1. Expected number = probability × number of spins
2. 0.4 × 50 = 20
Answer: 20
Q8.Two fair coins are flipped. Find the probability of getting two heads.
Show worked answer
1. List the outcomes: HH, HT, TH, TT, which is 4 outcomes
2. Only HH is two heads
3. P(two heads) = 1/4
Answer: 1/4
Q9.Two fair dice are rolled and the scores are added. Find the probability of a total of 7.
Show worked answer
1. A sample-space grid has 6 × 6 = 36 outcomes
2. Totals of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), which is 6 outcomes
3. P(7) = 6/36 = 1/6
Answer: 1/6
Q10.A drawing pin is dropped 120 times. It lands point up 36 times. Find the relative frequency of landing point up.
Show worked answer
1. Relative frequency = times it happened ÷ number of trials
2. 36 ÷ 120 = 0.3
Answer: 0.3

Can you do these?

Find a probability as a fraction, decimal or percentage
Use P(not A) = 1 − P(A) and complete a probability table
Work out an expected number of results
List outcomes for two events and use relative frequency

Tick them off on the printable checklist. Want more? The Core sections of our free probability notes cover the same maths (they are written for IGCSE, but the basics are the same).