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

OCR MEI A-Level Maths past-paper questions on 4.1 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 23 questions on Discrete distributions and the binomial, as a list

June 2025, Paper 2, Q11 (7 marks): Apples are sold in packets of 4. Ling and Sam are investigating the frequency, f, of the number of bruised apples in a packet, x. They each collect a random sam
June 2025, AS Paper 2, Q8 (4 marks): The probability function of a discrete random variable X is k r P X ( r ) , 1 2 3 4 , , , , = = = r where k is a constant. (a) Determine the value of k. [2] Two
June 2024, Paper 2, Q6 (5 marks): The probability distribution of the discrete random variable X is shown in the table. x 0 1 2 3 P ( X x ) 0.2 a 3a 0.4 = (a) Calculate the value of the constant
June 2024, AS Paper 2, Q15 (7 marks): Ali and Sam are playing a game in which Ali tosses a coin 5 times. If there are 4 or 5 heads, Ali wins the game. Otherwise Sam wins the game. They decide to pla
June 2023, Paper 2, Q4 (5 marks): A biased octagonal dice has faces numbered from 1 to 8. The discrete random variable X is the score obtained when the dice is rolled once. The probability distr
June 2023, Paper 2, Q18 (11 marks): Riley is investigating the daily water consumption, in litres, of his household. He records the amount used for a random sample of 120 days from the previous tw
June 2023, AS Paper 2, Q9 (6 marks): The table shows the probability distribution for the discrete random variable X. x 1 2 3 4 5 P ( X x ) 0.1 0.3 q 2q 3q = You are given that q is a positive cons
June 2022, Paper 2, Q11 (10 marks): A die in the form of a dodecahedron has its faces numbered from 1 to 12. The die is biased so that the probability that a score of 12 is achieved is different f
June 2022, AS Paper 2, Q1 (1 mark): The probability distribution for the discrete random variable X is shown below. x 1 2 3 4 5 X x 0.2 0.15 a 0.27 0.14 P ( ) = Find the value of a. [1]
November 2021, Paper 2, Q5 (3 marks): It is known that 40% of people in Britain carry a certain gene. A random sample of 32 people is collected. (a) Calculate the probability that exactly 12 people
November 2021, Paper 2, Q13 (7 marks): At a certain factory Christmas tree decorations are packed in boxes of 10. The quality control manager collects a random sample of 100 boxes of decorations and
November 2021, Paper 2, Q15 (11 marks): =/ r 1 15 (a) Show that 0 99 . - 0 01 . 1 . [3] = # r 1 Kofi is a very good table tennis player. Layla is determined to beat him. Every week they play one match
November 2021, AS Paper 2, Q2 (2 marks): Mia rolls a six-sided die 24 times and records the scores. She displays her results in a vertical line chart. This is shown in Fig. 2.1. Scores on a six-sided d
November 2021, AS Paper 2, Q6 (6 marks): The probability distribution for the discrete random variable X is shown below. x 0 1 2 3 3p2 0.5p2 +2p 1.5p2 + 0.5p 1.5p P(X = x) (a) Determine the value of p.
November 2021, AS Paper 2, Q12 (8 marks): A manufacturer of steel rods checks the length of each rod in randomly selected batches of 10 rods. 100 batches of 10 rods are checked and x, the number of rods
November 2020, Paper 2, Q12 (15 marks): In this question you must show detailed reasoning. A 5-sided spinner can give scores of 1, 2, 3, 4 or 5. After observing a large number of spins, Elaine models
November 2020, AS Paper 2, Q4 (4 marks): In a certain country it is known that 11% of people are left-handed. (a) Calculate the probability that, in a random sample of 98 people from this country, 5 or
June 2019, Paper 2, Q1 (4 marks): Fig. 1 shows the probability distribution of the discrete random variable X. x 1 2 3 4 5 X x 0.2 0.1 k 2k 4k P ( ) = Fig. 1 (a) Find the value of k. [2] (b) Fin
June 2019, Paper 2, Q15 (6 marks): You must show detailed reasoning in this question. The screenshot in Fig. 15 shows the probability distribution for the continuous random variable X, 2 where X
June 2019, AS Paper 2, Q8 (10 marks): According to the latest research there are 19.8 million male drivers and 16.2 million female drivers on the roads in the UK. (a) A driver in the UK is selected
June 2018, Paper 2, Q8 (4 marks): Every morning before breakfast Laura and Mike play a game of chess. The probability that Laura wins is 0.7. The outcome of any particular game is independent of
June 2018, Paper 2, Q11 (6 marks): The discrete random variable X takes the values 0, 1, 2, 3, 4 and 5 with probabilities given by the formula P(X = x) = k(x + 1)(6 ‒ x) . (i) Find the value of k
June 2018, AS Paper 2, Q4 (5 marks): The probability distribution of the discrete random variable X is given in Fig. 4. r 0 1 2 3 4 P(X = r) 0.2 0.15 0.3 k 0.25 Fig. 4 (i) Find the value of k. [2]

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