GCSE Maths Higher: Probability practice questions
Ten free GCSE Maths Higher tier questions on independent events, without replacement, Venn diagrams, conditional probability, tree diagrams and counting, each with a worked solution. Suitable for AQA, Edexcel and OCR.
Original questions written by Studoli tutors in the style of the GCSE exam. They are not official past questions.
Timed mode
10 questions in 15 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.
Topic: Independent events
1. A and B are independent. P(A) = 0.6 and P(B) = 0.5. Find P(A and B).
Solution
B. 0.3
- For independent events, P(A and B) = P(A) × P(B).
- 0.6 × 0.5 = 0.3.
Topic: Without replacement
2. A bag holds 4 red and 6 blue balls. Two are taken without replacement. Find P(both blue).
Solution
A. 1/3
- P(first blue) = 6/10. One blue is gone, so P(second blue) = 5/9.
- 6/10 × 5/9 = 30/90 = 1/3.
Topic: At least one
3. A fair dice is rolled twice. Find P(at least one six).
Solution
D. 11/36
- P(no six) = 5/6 × 5/6 = 25/36.
- P(at least one six) = 1 − 25/36 = 11/36.
Topic: Venn diagrams
4. n(ξ) = 30, n(A) = 12, n(B) = 15 and n(A ∩ B) = 5. Find P(A ∪ B).
Solution
C. 11/15
- n(A ∪ B) = 12 + 15 − 5 = 22.
- P(A ∪ B) = 22/30 = 11/15.
Topic: Conditional probability
5. Of 40 students, 25 study French, and 10 of those also study Spanish. A French student is chosen at random. Find P(they study Spanish).
Solution
B. 2/5
- Only the 25 French students count.
- 10 of them study Spanish: 10/25 = 2/5.
Topic: Tree diagrams
6. P(rain on Monday) = 0.3. If it rains on Monday, P(rain on Tuesday) = 0.6; if not, it is 0.2. Find P(rain on Tuesday).
Solution
A. 0.32
- Rain both days: 0.3 × 0.6 = 0.18.
- No rain Monday, rain Tuesday: 0.7 × 0.2 = 0.14.
- Add the two routes: 0.18 + 0.14 = 0.32.
Topic: Arrangements
7. In how many ways can the letters of MATHS be arranged?
Solution
D. 120
- There are 5 different letters, so 5! arrangements.
- 5 × 4 × 3 × 2 × 1 = 120.
Topic: Product rule
8. A menu has 4 starters, 6 mains and 3 desserts. How many different three-course meals are there?
Solution
C. 72
- Multiply the choices for each course.
- 4 × 6 × 3 = 72.
Topic: Combined events
9. Two fair dice are rolled. Find the probability that the total is 7.
Solution
B. 1/6
- There are 36 equally likely outcomes.
- Totals of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), which is 6 outcomes.
- 6/36 = 1/6.
Topic: Expected frequency
10. Two sets of traffic lights work independently. Each is red with probability 0.4. On 200 journeys, how many times would you expect both to be red?
Solution
A. 32
- P(both red) = 0.4 × 0.4 = 0.16.
- Expected number = 0.16 × 200 = 32.
0 of 10 answered