Discrete distributions and the binomial: OCR A‑Level Maths questions

OCR A-Level Maths past-paper questions on 2.04.1 Discrete distributions and the binomial, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 19 questions on Discrete distributions and the binomial, as a list

June 2025, Paper 2, Q10 (5 marks): 1). 10 (a) The random variable W has the distribution B(12, 3 Find P(W H 7). [2] (b) The random variable X has the distribution N(45, 42). Find P(X 2 50). [1] (
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 2024, Paper 2, Q8 (6 marks): Sweets from a certain manufacturer are sold in packets. Thirty per cent of the sweets are orange, and these are randomly distributed amongst the packets. Each p
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, Q4 (4 marks): (a) Write down the term in b5 in the expansion of ( b 12 4 a ) . [1] + (b) A variable X has a binomial distribution such that P(X = 5) is given by the term in p
June 2023, Paper 2, Q9 (6 marks): A school contains 500 students in years 7 to 11 and 250 students in years 12 and 13. A random sample of 20 students is selected to represent the school at a par
June 2022, AS Paper 1, Q9 (10 marks): Last year, market research showed that 8% of adults living in a certain town used a particular local coffee shop. Following an advertising campaign, it was expe
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, 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, Q12 (7 marks): 1). The probabilities ( 12 The variable X has the distribution B(50, 6 P X r ) for r = 0 to 50 are given = b n by the terms of the expansion of ( a ) for specif
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, 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, Paper 2, Q13 (5 marks): It is known that 26% of adults in the UK use a certain app. A researcher selects a random sample of 5000 adults in the UK. The random variable X is defined as t
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, Paper 2, Q13 (12 marks): In this question you must show detailed reasoning. The probability that Paul’s train to work is late on any day is 0.15, independently of other days. (i) The nu
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
June 2018, AS Paper 1, Q11 (5 marks): The probability that Janice sees a kingfisher on any particular day is 0.3. She notes the number, X, of days in a week on which she sees a kingfisher. (i) State

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