Discrete uniform and binomial in further statistics: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 1.4 Discrete uniform and binomial in further statistics, 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 40 questions on Discrete uniform and binomial in further statistics, as a list

June 2025, Statistics Major, Q1 (7 marks): A fair eight sided dice has its sides labelled 1, 2, …, 8. The random variable X represents the score when the dice is rolled once. (a) Find ( P X 2 4 ) . [1] (
June 2025, Statistics Major, Q4 (12 marks): Gabi is practising basketball. On each attempt to score a basket, the probability that Gabi scores is modelled as 0.4. It is assumed that each attempt is indepe
June 2025, Statistics Major, Q10 (13 marks): Two independent random variables, X and Y, have distributions B(6, 0.4) and B(3, 0.4) respectively. The random variable T X ( Y Y ) where Y1 and Y2 are two inde
June 2025, Statistics Major, Q12 (6 marks): The random variable X takes the value 1 with probability p and the value 0 with probability 1 - p. You are given that E(X ) = p and Var(X ) = p - p2. The random
June 2025, Statistics Minor, Q4 (7 marks): The discrete random variable, X, has a uniform distribution over the values {5, 6, ..., n}. (a) In this question you must show detailed reasoning. In part (a) y
June 2025, Statistics Minor, Q5 (13 marks): Long-term data collected at a certain farm indicates that 30% of eggs that it produces are large and the rest are categorised as medium. Eggs are collected in b
June 2025, AS Statistics A, Q2 (7 marks): The probability distribution of a discrete random variable X is given in the table. x 0 1 2 3 1 1 1 P ( X x ) a = 6 3 10 (a) Find the value of a. [1] The probab
June 2025, AS Statistics A, Q3 (10 marks): The discrete random variable Q has the distribution Geo(0.3). (a) Find ( P Q 2 ) . [1] = (b) Determine ( P Q 5 ) . [2] G The discrete random variable R has a un
June 2024, Statistics Major, Q11 (11 marks): The discrete random variable X has a uniform distribution over the set of all integers between 25 and n inclusive, where n is a positive integer with n 2 25 . J
June 2024, Statistics Minor, Q2 (7 marks): The sides of a fair 12-sided spinner are labelled 1, 2, ..., 12. The spinner is spun and X is the random variable denoting the number on the side of the spinner
June 2024, AS Statistics A, Q2 (9 marks): In a game of chance there are 32 slots, numbered 1 to 32, and on each turn a ball lands in one of them. You may assume that the process is completely random. Yo
June 2024, AS Statistics A, Q6 (10 marks): A bank monitors the amounts of cash withdrawn from a cash machine. It categorises any withdrawal of an amount of £50 or less as ‘small’ and any withdrawal of an
June 2023, Statistics Major, Q1 (10 marks): A website simulates the outcome of throwing four fair dice. Ten thousand people take part in a challenge using the website in which they have one attempt at get
June 2023, Statistics Major, Q3 (10 marks): A tennis player is practising her serve. Each time she serves, she has a 55% chance of being successful (getting the serve in the required area without hitting
June 2023, Statistics Major, Q11 (9 marks): The random variable X takes the value 1 with probability p and the value 0 with probability 1 - . p (a) Find each of the following. • E(X) • Var(X) [3] 2 (b) Th
June 2023, Statistics Minor, Q7 (6 marks): The discrete random variable X has a uniform distribution over the set of all integers between 100 and n inclusive, where n is a positive integer with n 2 100.
June 2023, AS Statistics A, Q3 (7 marks): At a pottery which manufactures mugs, it is known that 5% of mugs are faulty. The mugs are produced in batches of 20. Faults are modelled as occurring randomly
June 2023, AS Statistics A, Q6 (15 marks): An eight-sided dice has its faces numbered 1, 2, …, 8. (a) In this part of the question you should assume that the dice is fair. (i) State the probability that,
June 2022, Statistics Major, Q4 (5 marks): A pack of k cards is labelled 1, 2, …, k. A card is drawn at random from the pack. The random variable X represents the number on the card. (a) Given that k 2 1
June 2022, Statistics Major, Q7 (8 marks): Amir is trying to thread a needle. On each attempt the probability that he is successful is 0.3, independently of any other attempt. The random variable X repre
June 2022, Statistics Major, Q9 (11 marks): The random variable X has a discrete uniform distribution over the values {0, 1, 2, …, 20}. (a) Find P(X G 7). [1] (b) Find each of the following. • E(X) • Var(
June 2022, Statistics Minor, Q6 (7 marks): The random variable X has a uniform distribution over the values {1, 4, 7, …, 3n - 2}, where n is a positive integer. (a) Determine Var(X ) in terms of n. [3] (
June 2022, AS Statistics A, Q4 (6 marks): A random number generator generates integers between 1 and 50 inclusive, with each number having an equal probability of being generated. (a) State the probabil
November 2021, Statistics Major, Q3 (10 marks): In air traffic management, air traffic controllers send radio messages to pilots. On receiving a message, the pilot repeats it back to the controller to check t
November 2021, Statistics Major, Q9 (6 marks): The discrete random variable X has a uniform distribution over the set of all integers between -n and n inclusive, where n is a positive integer. 1 (a) Given th
November 2021, Statistics Minor, Q6 (7 marks): A lottery has tickets numbered 1 to n inclusive, where n is a positive integer. The random variable X denotes the number on a ticket drawn at random. 1 (a) Dete
November 2021, AS Statistics A, Q1 (4 marks): The random variable X represents the clutch size (the number of eggs laid) by female birds of a particular species. The probability distribution of X is given i
November 2021, AS Statistics A, Q5 (7 marks): A fair spinner has five faces, labelled 0, 1, 2, 3, 4. (a) State the distribution of the score when the spinner is spun once. [2] (b) Determine the probability
November 2021, AS Statistics B, Q2 (10 marks): Natasha is investigating binomial distributions. She constructs the spreadsheet in Fig. 2 which shows the first 3 and last 4 rows of a simulation involving two
November 2020, Statistics Major, Q9 (16 marks): A supermarket sells trays of peaches. Each tray contains 10 peaches. Often some of the peaches in a tray are rotten. The numbers of rotten peaches in a random s
November 2020, Statistics Minor, Q6 (9 marks): (a) The random variable X has a uniform distribution over the values {1, 2, …, n}. Show that 2 - 1 Var(X ) is given by ( n 1 ) . [3] 12 (b) The random variable
November 2020, AS Statistics A, Q3 (8 marks): A child is trying to draw court cards from an ordinary pack of 52 cards (court cards are Kings, Queens and Jacks; there are 12 in a pack). She draws cards, one
November 2020, AS Statistics A, Q4 (8 marks): A fair 8-sided dice has faces labelled 1, 2, …, 8. The random variable X represents the score when the dice is rolled once. (a) State the distribution of X. [2]
June 2019, Statistics Minor, Q1 (7 marks): In a game at a charity fair, a spinner is spun 4 times. On each spin the chance that the spinner lands on a score of 5 is 0.2. The random variable X represents
June 2019, Statistics Minor, Q6 (7 marks): The discrete random variable X has a uniform distribution over { , n n 1 , ..., 2 n } . + 3 (a) Given that n is odd, find ( P X 1 n ) . [1] 2 3 (b) Given instea
June 2019, AS Statistics A, Q2 (9 marks): Almost all plants of a particular species have red flowers. However on average 1 in every 1500 plants of this species have white flowers. A random sample of 200
June 2019, AS Statistics A, Q3 (9 marks): A fair 8-sided dice has faces labelled 10, 20, 30, ..., 80. (a) State the distribution of the score when the dice is rolled once. [2] (b) Write down the probabi
June 2019, AS Statistics A, Q5 (13 marks): A researcher is investigating births of females and males in a particular species of animal which very often produces litters of 7 offspring. The table shows so
June 2018, AS Statistics A, Q2 (10 marks): In a quiz, competitors have to match 5 landmarks to the 5 British counties which the landmarks are in. The random variable X represents the number of correct ma
June 2018, AS Statistics A, Q4 (9 marks): The probability that an expert darts player hits the bullseye on any throw is 0.12, independently of any other throw. The player throws darts at the bullseye un

Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR MEI A-Level Further Maths past papers.

The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.

841 questions