GCSE MATHS PRACTICE

GCSE Probability Questions

Probability runs from 0 (impossible) to 1 (certain). For equally likely outcomes, divide the number of favourable outcomes by the total number of outcomes. An event and its complement have probabilities that add to 1. For a simple combined event, list the possible outcomes carefully. These samples introduce core probability rather than the whole course.

Updated 11 October 2026

Worked example

A bag contains 5 red, 3 blue and 4 green counters. One counter is chosen at random. Find the probability that it is not blue.

There are 5 + 3 + 4 = 12 counters, all equally likely to be chosen.
There are 5 + 4 = 9 counters that are not blue, so the probability is 912 = 34.
Check using the complement: 1 − 312 = 34.

Answer: 34

Practice questions

1
A fair six-sided die is rolled. Find the probability of rolling a number greater than 6.
2
A spinner has 10 equal sectors numbered 1 to 10. Find the probability of landing on a multiple of 3.
3
The probability that a bus is late is 27. Find the probability that it is not late.
4
A fair coin is tossed and a fair six-sided die is rolled independently. Find the probability of getting heads and a number greater than 4.

Show answers

1. 0 (impossible)
2. 310
3. 57
4. 16

Common mistakes

Using the favourable count as the total — The denominator must count all equally likely outcomes.
Forgetting the complement — Not happening has probability 1 minus the probability of happening.
Assuming outcomes are equally likely — Check the conditions before using favourable outcomes divided by total outcomes.

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GCSE Probability Questions

Updated 11 October 2026

Worked example

A bag contains 5 red, 3 blue and 4 green counters. One counter is chosen at random. Find the probability that it is not blue.

There are 5 + 3 + 4 = 12 counters, all equally likely to be chosen.

There are 5 + 4 = 9 counters that are not blue, so the probability is 912 = 34.

Check using the complement: 1 − 312 = 34.

Answer: 34

Practice questions

A fair six-sided die is rolled. Find the probability of rolling a number greater than 6.

A spinner has 10 equal sectors numbered 1 to 10. Find the probability of landing on a multiple of 3.

The probability that a bus is late is 27. Find the probability that it is not late.

A fair coin is tossed and a fair six-sided die is rolled independently. Find the probability of getting heads and a number greater than 4.

Show answers

1. 0 (impossible)
2. 310
3. 57
4. 16

Common mistakes

Using the favourable count as the total — The denominator must count all equally likely outcomes.

Forgetting the complement — Not happening has probability 1 minus the probability of happening.

Assuming outcomes are equally likely — Check the conditions before using favourable outcomes divided by total outcomes.

GCSE Probability Questions

Worked example

Practice questions

Common mistakes

Related resources

GCSE Probability Questions

Worked example

Practice questions

Common mistakes

Related resources