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

Edexcel A-Level Maths past-paper questions on 4.1 Discrete distributions and the binomial, 2010–2025, 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, Statistics, Q3 (6 marks): A manufacturer makes components for the car industry. On average 1.5% of the components made are defective. (a) Using a suitable model, find the probability tha
June 2025, Statistics, Q6 (11 marks): The discrete random variable R takes even integer values from 2 to 2n inclusive. The probability distribution of R is given by P 2, 4, 6, … , 2 r R r r n k wher
June 2025, AS Statistics, Q1 (3 marks): The random variable X ~ B(20, 0.37) (a) Find P(X = 8) (1) (b) Find P(X  5) (1) (c) Find P(X  5.7) (1)
June 2025, AS Statistics, Q3 (9 marks): A bag contains red counters, green counters and white counters only. The table shows the proportion of each colour of counter that Elsa believes to be in the ba
June 2024, Statistics, Q1 (11 marks): Xian rolls a fair die 10 times. The random variable X represents the number of times the die lands on a six. (a) Using a suitable distribution for X, find (i) P
June 2024, AS Statistics, Q4 (8 marks): The random variable X ~ B(27, 0.35) (a) Find (i) P(X = 10) (ii) P(12  X < 15) (3) Historical records show that the proportion of defective items produced by a
June 2024, AS Statistics, Q5 (8 marks): A biased 4-sided spinner has the numbers 6, 7, 8 and 10 on it. The discrete random variable X represents the score when the spinner is spun once and has the fol
June 2023, Statistics, Q2 (9 marks): A machine fills packets with sweets and 1 7 of the packets also contain a prize. The packets of sweets are placed in boxes before being delivered to shops. Ther
June 2023, Statistics, Q5 (8 marks): Tisam is playing a game. She uses a ball, a cup and a spinner. The random variable X represents the number the spinner lands on when it is spun. The probability
June 2023, AS Statistics, Q5 (8 marks): Julia selects 3 letters at random, one at a time without replacement, from the word V A R I A N C E The discrete random variable X represents the number of time
June 2022, Statistics, Q1 (6 marks): George throws a ball at a target 15 times. Each time George throws the ball, the probability of the ball hitting the target is 0.48 The random variable X repres
June 2022, AS Statistics, Q2 (7 marks): A manufacturer of sweets knows that 8% of the bags of sugar delivered from supplier A will be damp. A random sample of 35 bags of sugar is taken from supplier A
June 2022, AS Statistics, Q5 (8 marks): Manon has two biased spinners, one red and one green. The random variable R represents the score when the red spinner is spun. The random variable G represents
November 2021, Statistics, Q1 (7 marks): (a) State one disadvantage of using quota sampling compared with simple random sampling. (1) In a university 8% of students are members of the university dance
November 2021, Statistics, Q6 (7 marks): The discrete random variable X has the following probability distribution x a b c P(X = x) log36 a log36 b log36 c where • a, b and c are distinct integers (a <
November 2021, AS Statistics, Q4 (10 marks): A nursery has a sack containing a large number of coloured beads of which 14% are coloured red. Aliya takes a random sample of 18 beads from the sack to make a
November 2020, Statistics, Q4 (10 marks): The discrete random variable D has the following probability distribution d 10 20 30 40 50 P (D = d ) k 10 k 20 k 30 k 40 k 50 where k is a constant. (a) Show t
November 2020, AS Statistics, Q3 (6 marks): In a game, a player can score 0, 1, 2, 3 or 4 points each time the game is played. The random variable S, representing the player’s score, has the following pro
November 2020, AS Statistics, Q5 (8 marks): Afrika works in a call centre. She assumes that calls are independent and knows, from past experience, that on each sales call that she makes there is a probabi
June 2019, Statistics, Q4 (9 marks): Magali is studying the mean total cloud cover, in oktas, for Leuchars in 1987 using data from the large data set. The daily mean total cloud cover for all 184 d
June 2019, AS Statistics, Q3 (6 marks): A fair 5-sided spinner has sides numbered 1, 2, 3, 4 and 5 The spinner is spun once and the score of the side it lands on is recorded. (a) Write down the name o
June 2018, Statistics and Mechanics, Q1 (5 marks): Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution. (a) Write down
June 2018, Statistics and Mechanics, Q3 (11 marks): In an experiment a group of children each repeatedly throw a dart at a target. For each child, the random variable H represents the number of times the dart hit

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