plumiDiscrete distributions: OCR A‑Level Further Maths questions
Every OCR A-Level Further Maths exam question on FS.1 Discrete distributions, 2018–2025, with its mark scheme and examiner’s report.
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![June 2024 AS Statistics, question 1: The random variable W can take values 1, 2 or 3 and has a discrete uniform distribution. (a) Write down the value of E(2W ). [1] (b) Find the value of Var(2W ).](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y53201-jun24-01-qp.webp?v=3)
All 53 questions on Discrete distributions, as a list
- June 2025, Statistics, Q2 (7 marks): of a forest can be modelled by the 2 The number of trees of a particular species found in km 1 distribution Po m . ( ) The forest consists of two regions, A and
- June 2025, Statistics, Q9 (8 marks): A set of 50 independent observations of a discrete random variable X, with an unknown distribution, is found. (a) The mean and variance of the 50 observations a
- June 2025, AS Statistics, Q2 (10 marks): On any day, flights of helicopters and aeroplanes pass within sight of a certain building only during a daytime period of 12 hours, from 7.00 am to 7.00 pm. The
- June 2025, AS Statistics, Q5 (9 marks): The probability distribution of a discrete random variable U is given in the table. u 0 1 2 3 U u r 0.3 p 0 5 - . p P ( ) = (a) Find the value of the constant r
- June 2025, AS Statistics, Q6 (13 marks): A spinner has probability 0.2 of landing on an edge coloured blue. The spinner is spun repeatedly. The number of spins required, up to and including the first s
- June 2024, Statistics, Q1 (8 marks): A discrete random variable X has the following distribution, where a, b and c are constants. x 0 1 2 3 X x a b c 0.1 P ( ) = It is given that ( ) E X 1 25 . and
- June 2024, Statistics, Q5 (12 marks): Some bird-watchers study the song of chaffinches in a particular wood. They investigate whether the number, N, of separate bursts of song in a 5 minute period c
- June 2024, Statistics, Q6 (11 marks): A bag contains 6 identical blue counters and 5 identical yellow counters. (a) Three counters are selected at random, without replacement. Find the probability t
- June 2024, AS Statistics, Q1 (8 marks): The random variable W can take values 1, 2 or 3 and has a discrete uniform distribution. (a) Write down the value of E(2W ). [1] (b) Find the value of Var(2W ).
- June 2024, AS Statistics, Q4 (12 marks): In this question you must show detailed reasoning. The random variables X and Y denote the number of telephone calls and the number of e-mails, respectively, re
- June 2024, AS Statistics, Q6 (12 marks): Anika walks along a street that contains parked cars. The number of cars that Anika passes, up to and including the first car that is white, is denoted by X. (a
- June 2023, Statistics, Q1 (8 marks): A certain section of a library contains several thousand books. A lecturer is looking for a book that refers to a particular topic. The lecturer believes that o
- June 2023, Statistics, Q3 (6 marks): The discrete random variable W has the distribution U(11). The independent discrete random variable V has the distribution U(5). (a) It is given that, for const
- June 2023, AS Statistics, Q1 (7 marks): A radar device is used to detect flaws in motorway roads before they become dangerous. The number of flaws in a 1 km stretch of motorway is denoted by X. It may
- June 2023, AS Statistics, Q2 (7 marks): A music lover has 30 CDs arranged in a random order in a line on a shelf. Of these CDs, 7 are classed as Baroque, 10 as Classical and 13 as Romantic. (a) Determ
- June 2023, AS Statistics, Q4 (7 marks): A discrete random variable W has the probability distribution shown in the following table, in which a and b are constants. w 58 59 60 61 62 63 a b 0.2 0.2 0.1
- June 2023, AS Statistics, Q6 (12 marks): A machine is used to toss a coin repeatedly. Rosa believes that the outcome of each toss made by the machine is not independent of the previous toss. Rosa gets
- June 2023, AS Statistics, Q7 (10 marks): A town council is planning to introduce a new set of parking regulations. An interviewer contacts randomly chosen people in the town and asks them whether they
- June 2022, Statistics, Q1 (5 marks): A researcher wishes to find people who say that they support a specific plan. Each day the researcher interviews people at random, one after the other, until th
- June 2022, Statistics, Q3 (8 marks): In this question you must show detailed reasoning. A discrete random variable V has the following probability distribution, where p and q are constants. v 0 1 2
- June 2022, Statistics, Q4 (9 marks): The manager of a car breakdown service uses the distribution Po(2.7) to model the number of punctures, R, in a 24‑hour period in a given rural area. The manager
- June 2022, AS Statistics, Q3 (9 marks): A discrete random variable X has the following probability distribution. x 1 2 3 4 p 0.31 0.3 P(X = x) p2 (a) Determine the value of p. [3] (b) It is given that
- June 2022, AS Statistics, Q5 (9 marks): The manager of an emergency response hotline believes that calls are made to the hotline independently and at constant average rate throughout the day. From a s
- June 2022, AS Statistics, Q6 (10 marks): A teacher has 10 different mathematics books. Of these books, 5 are on Algebra, 3 are on Calculus and 2 are on Trigonometry. The teacher chooses 5 of the books
- June 2022, AS Statistics, Q7 (10 marks): Each of three students, X, Y and Z, was given an identical pack of 48 cards, of which 12 cards were red and 36 were blue. They were each told to carry out a dif
- November 2021, Statistics, Q2 (7 marks): A discrete random variable D has the following probability distribution, where a is a constant. d 0 2 4 6 a 0.1 0.3 0.2 P(D = d ) Determine the value of Var(3D
- November 2021, Statistics, Q3 (9 marks): In a large collection of coloured marbles of identical size, the proportion of green marbles is p. One marble is chosen randomly, its colour is noted, and it is
- November 2021, AS Statistics, Q1 (8 marks): The discrete random variable A has the following probability distribution. a 1 2 5 10 20 0.3 0.1 0.1 0.2 0.3 P(A = a) (a) Find the value of E(A). [2] (b) Determ
- November 2021, AS Statistics, Q4 (4 marks): Two random variables X and Y have the distributions B(m, p) and B(n, p) respectively, where p 2 0 . It is known that • E(Y) = 2E(X) • Var(Y) = 1.2E(X). Determin
- November 2021, AS Statistics, Q5 (6 marks): The discrete random variable X has a geometric distribution. It is given that Var X ( ) 20 . = Determine ( P X 7 ) . [6] H
- November 2021, AS Statistics, Q7 (8 marks): The 20 members of a club consist of 10 Town members and 10 Country members. (a) All 20 members are arranged randomly in a straight line. Determine the probabili
- November 2021, AS Statistics, Q8 (11 marks): (a) A substance emits particles randomly at a constant average rate of 3.2 per minute. A second substance emits particles randomly, and independently of the fir
- November 2020, Statistics, Q4 (7 marks): The random variable X is equally likely to take any of the n integer values from m + to m 1 n + inclusive. It is given that ( E 3 X ) 30 and Var ( 3 X ) 36 . =
- November 2020, Statistics, Q5 (11 marks): 26 cards are each labelled with a different letter of the alphabet, A to Z. The letters A, E, I, O and U are vowels. (a) Five cards are selected at random witho
- November 2020, Statistics, Q6 (11 marks): The numbers of CD players sold in a shop on three consecutive weekends were 7, 6 and 2. It may be assumed that sales of CD players occur randomly and that nobod
- November 2020, Statistics, Q7 (10 marks): A biased spinner has five sides, numbered 1 to 5. Elmer spins the spinner repeatedly and counts the number of spins, X, up to and including the first time that
- November 2020, AS Statistics, Q2 (8 marks): Every time a spinner is spun, the probability that it shows the number 4 is 0.2, independently of all other spins. (a) A pupil spins the spinner repeatedly unti
- November 2020, AS Statistics, Q6 (10 marks): A statistician investigates the number, F, of signal failures per week on a railway network. (a) The statistician assumes that signal failures occur randomly. E
- November 2020, AS Statistics, Q7 (7 marks): A bag contains 2m yellow and m green counters. Three counters are chosen at random, without 28 . replacement. The probability that exactly two of the three coun
- June 2019, Statistics, Q2 (4 marks): The average numbers of cars, lorries and buses passing a point on a busy road in a period of 30 minutes are 400, 80 and 17 respectively. (a) Assuming that the n
- June 2019, Statistics, Q3 (6 marks): Six red counters and four blue counters are arranged in a straight line in a random order. Find the probability that (a) no blue counter has fewer than two red
- June 2019, Statistics, Q7 (10 marks): 7 The random variable D has the distribution Geo(p). It is given that Var D ( ) . = 9 Determine (a) Var ( 3 D 5 ) , [1] + (b) E ( 3 D 5 ) , [6] + (c) P ( D 2 E
- June 2019, Statistics, Q9 (14 marks): The continuous random variable T has cumulative distribution function ' 0 t 1 0 , F t ( ) = 0 25 . t 1 e t 0 . - - H (a) Find the cumulative distribution functi
- June 2019, AS Statistics, Q1 (9 marks): When a spinner is spun, the outcome is equally likely to be 1, 2 or 3. In a competition, the spinner is spun twice and the outcomes are added to give a total sc
- June 2019, AS Statistics, Q2 (6 marks): On any day, the number of orders received in one randomly chosen hour by an online supplier can be modelled by the distribution Po(120). (a) Find the probabilit
- June 2019, AS Statistics, Q4 (7 marks): The members of a team stand in a random order in a straight line for a photograph. There are four men and six women. (a) Find the probability that all the men a
- June 2019, AS Statistics, Q6 (9 marks): A bag contains a mixture of blue and green beads, in unknown proportions. The proportion of green beads in the bag is denoted by p. (a) Sasha selects 10 beads a
- June 2019, AS Statistics, Q8 (7 marks): Alex claims that he can read people’s minds. A volunteer, Jane, arranges the integers 1 to n in an order of Jane’s own choice and Alex tells Jane what order he
- June 2018, AS Statistics, Q1 (8 marks): A book reviewer estimates that the probability that he receives a delivery of books to review on any one weekday is 0.1. The first weekday in September on which
- June 2018, AS Statistics, Q2 (8 marks): The probability distribution for the discrete random variable W is given in the table. w 1 2 3 4 ^ h x2 P W w 0.25 0.36 x = ^ h (i) Show that W [7] Var 0 8571 .
- June 2018, AS Statistics, Q3 (6 marks): In the manufacture of fibre optical cable (FOC), flaws occur randomly. Whether any point on a cable is flawed is independent of whether any other point is flawe
- June 2018, AS Statistics, Q5 (8 marks): (i) A team of 9 is chosen at random from a class consisting of 8 boys and 12 girls. Find the probability that the team contains no more than 3 girls. [4] (ii) A
- June 2018, AS Statistics, Q6 (5 marks): In this question you must show detailed reasoning. ^ h The random variable T has a binomial distribution. It is known that T E 5 625 . and the standard deviatio
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