plumiProbability: OCR A‑Level Maths questions
Every OCR A-Level Maths exam question on S.3 Probability, 2018–2025, with its mark scheme and examiner’s report.
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All 22 questions on Probability, as a list
- June 2025, Paper 2, Q12 (7 marks): Sam has 9 cards, each with a different non-zero digit printed on it. 1 2 3 4 5 6 7 8 9 Sam chooses 5 cards at random and places them in a random order in a stra
- June 2025, Paper 2, Q15 (4 marks): The probability distribution of the random variable X is modelled as follows. • P(X = 1) = p where p is a constant. • P(X = x) = 2P(X = x - 1) for x = 2, 3, 4.
- June 2025, AS Paper 1, Q11 (4 marks): A spinner has sides numbered 1, 2, 3, 4. When the spinner is spun the score is given by the number of the side on which it lands. The spinner is biased, as show
- June 2024, Paper 2, Q12 (4 marks): Ryan has to choose one student at random from a group of 11 students. Ryan makes the choice using a single throw of two fair, six-sided dice, together with the
- June 2024, Paper 2, Q14 (8 marks): For a certain value of the constant p, the random variable X has the probability distribution given in the table. x 1 2 3 4 1 1 X = x p p2 P ( ) p 6 2 Two indep
- June 2024, AS Paper 1, Q10 (4 marks): There are 60 members in a sports club. The table shows the numbers of members in various categories. Beginner Advanced Junior 35 5 Senior 7 13 A member of the s
- June 2023, Paper 2, Q14 (7 marks): In this question you must show detailed reasoning. A disease that affects trees shows no visible evidence for the first few years after the tree is infected. A
- June 2023, AS Paper 1, Q9 (4 marks): In a survey, 50 people were asked whether they had passed A-level English and whether they had passed A-level Mathematics. The numbers of people in various cate
- June 2022, Paper 2, Q7 (8 marks): It is given that any integer can be expressed in the form m 3 + , where m is an integer and r r is 0, 1 or 2. Use this fact to answer the following. (a) By cons
- June 2022, Paper 2, Q13 (10 marks): There are 25 students in a class. • The number of students who study both History and English is 3. • The number of students who study neither History nor Engli
- June 2022, AS Paper 1, Q11 (6 marks): Alex models the number of goals that a local team will score in any match as follows. More Number of goals 0 1 2 3 4 than 4 3 1 8 7 2 Probability 0 25 5 25 25 2
- November 2021, Paper 2, Q12 (13 marks): Anika and Beth are playing a game which consists of several points. • The probability that Anika will win any point is 0.7. • The probability that Beth will win
- November 2021, Paper 2, Q14 (11 marks): The probability distribution of a random variable X is modelled as follows. k * x 1 2 3 4 , , , , = x P ( X x ) = = 0 , otherwise where k is a constant. 12 (a)
- November 2021, AS Paper 1, Q10 (6 marks): Jane conducted a survey. She chose a sample of people from three towns, A, B and C. She noted the following information. 400 people were chosen. 230 people were
- November 2021, AS Paper 1, Q13 (7 marks): (a) The probability distribution of a random variable X is shown in the table, where p is a constant. x 0 1 2 3 1 1 p 3p P X ( x ) = 12 4 Two values of X are ch
- November 2020, Paper 2, Q13 (8 marks): Andy and Bev are playing a game. • The game consists of three points. • On each point, P(Andy wins) = 0.4 and P(Bev wins) = 0.6. • If one player wins two consec
- November 2020, Paper 2, Q15 (10 marks): In this question you must show detailed reasoning. The random variable X has probability distribution defined as follows. x * 15 2 x 2 3 4 5 , , , , = # 64 x !
- November 2020, AS Paper 1, Q11 (4 marks): In this question you must show detailed reasoning. A biased four-sided spinner has edges numbered 1, 2, 3, 4. When the spinner is spun, the probability that it
- June 2019, Paper 2, Q12 (12 marks): A random variable X has probability distribution defined as follows. * kx x 1 2 3 4 5 , , , , , = P ( X x ) = = 0 otherwise , where k is a constant. (a) Show th
- June 2019, AS Paper 1, Q12 (4 marks): The Venn diagram shows the numbers of students studying various subjects, in a year group of 100 students. History Geography 25 7 12 3 8 10 15 20 Psychology A s
- June 2018, Paper 2, Q12 (11 marks): The discrete random variable X takes values 1, 2, 3, 4 and 5, and its probability distribution is defined as follows. Z a x 1 , = ] ] 1 X x X x x P ( ) [ P ( 1
- June 2018, AS Paper 1, Q10 (5 marks): The probability distribution of a random variable X is given in the table. x 0 2 4 6 3 5 4 p p P(X = x) 8 16 (i) Find the value of p. [2] (ii) Two values of X a
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