هذه المجموعة متاحة بلغتها الأصلية.
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.
أسئلة أصلية كتبها مدرّسو Studoli بأسلوب امتحان GCSE. ليست أسئلة رسمية.
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.
الموضوع: Independent events
1. A and B are independent. P(A) = 0.6 and P(B) = 0.5. Find P(A and B).
الحل
B. 0.3
- For independent events, P(A and B) = P(A) × P(B).
- 0.6 × 0.5 = 0.3.
الموضوع: Without replacement
2. A bag holds 4 red and 6 blue balls. Two are taken without replacement. Find P(both blue).
الحل
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.
الموضوع: At least one
3. A fair dice is rolled twice. Find P(at least one six).
الحل
D. 11/36
- P(no six) = 5/6 × 5/6 = 25/36.
- P(at least one six) = 1 − 25/36 = 11/36.
الموضوع: Venn diagrams
4. n(ξ) = 30, n(A) = 12, n(B) = 15 and n(A ∩ B) = 5. Find P(A ∪ B).
الحل
C. 11/15
- n(A ∪ B) = 12 + 15 − 5 = 22.
- P(A ∪ B) = 22/30 = 11/15.
الموضوع: 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).
الحل
B. 2/5
- Only the 25 French students count.
- 10 of them study Spanish: 10/25 = 2/5.
الموضوع: 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).
الحل
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.
الموضوع: Arrangements
7. In how many ways can the letters of MATHS be arranged?
الحل
D. 120
- There are 5 different letters, so 5! arrangements.
- 5 × 4 × 3 × 2 × 1 = 120.
الموضوع: Product rule
8. A menu has 4 starters, 6 mains and 3 desserts. How many different three-course meals are there?
الحل
C. 72
- Multiply the choices for each course.
- 4 × 6 × 3 = 72.
الموضوع: Combined events
9. Two fair dice are rolled. Find the probability that the total is 7.
الحل
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.
الموضوع: 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?
الحل
A. 32
- P(both red) = 0.4 × 0.4 = 0.16.
- Expected number = 0.16 × 200 = 32.