plumiDiscrete distributions: OCR MEI A‑Level Further Maths questions
Every OCR MEI 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 2025 Statistics Major, question 1: 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] (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-jun25-01-qp.webp?v=3)
![June 2025 Statistics Minor, question 1: A discrete random variable, X, has a Poisson distribution with mean 4. (a) Write down the value of Var X . ( ) [1] (b) Find ( P X 3 ) . [1] = (c) Find ( P X 3 )](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y43201-jun25-01-qp.webp?v=3)
![June 2025 AS Statistics A, question 2: 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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41201-jun25-02-qp.webp?v=3)
![June 2025 AS Statistics A, question 3: 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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41201-jun25-03-qp.webp?v=3)
All 85 questions on Discrete distributions, 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, Q9 (13 marks): A consultant is modelling the number of trades per minute of a particular share in a stock exchange. The number of trades per minute in a random sample of 200 m
- 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, Q1 (6 marks): A discrete random variable, X, has a Poisson distribution with mean 4. (a) Write down the value of Var X . ( ) [1] (b) Find ( P X 3 ) . [1] = (c) Find ( P X 3 )
- June 2025, Statistics Minor, Q3 (8 marks): An archer fires arrows one by one at a target until an arrow hits the target. The number of arrows fired up to and including the arrow that hits the target is d
- 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, Statistics Minor, Q7 (12 marks): The probability function of the discrete random variable, X, is shown in the table. You are given that a, b and c are constants. x –1 0 1 P X ( x ) = a b c (a)
- 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 2025, AS Statistics A, Q6 (10 marks): The number of misprints in every 100 000 words of a book is denoted by the random variable X. The probability of any given word being misprinted is 0.000 11. Yo
- June 2024, Statistics Major, Q1 (5 marks): The number of insurance policy sales made per month by a salesperson is modelled by the random variable X, with probability distribution shown in the table. r 0
- June 2024, Statistics Major, Q2 (7 marks): The number of cars arriving per minute to queue at a drive-through fast-food restaurant is modelled by the random variable X. The standard deviation of X is 0.6
- 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, Q1 (7 marks): When a footballer takes a penalty kick the result is that either a goal is scored or a goal is not scored. It is known that, on average, a certain footballer sc
- 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, Statistics Minor, Q5 (12 marks): Over a long period of time, it is found that the mean number of mistakes made by a certain player when playing a particular piece of music is 5. The number of m
- June 2024, Statistics Minor, Q6 (9 marks): The probability distribution of a discrete random variable, X, is shown in the table below. x 0 1 2 P(X = x) 1 - a - b a b (a) Find E(X) in terms of a and b. [1
- June 2024, AS Statistics A, Q1 (7 marks): The probability distribution for a discrete random variable X is given in the table below. x 0 1 2 3 P ( X x ) 2c 3c 0 5 - . c c = (a) Find the value of c. [2]
- 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, Q3 (14 marks): A glassware factory produces a large number of ornaments each week. Just before they leave the factory, all the ornaments are checked and some may be found to b
- 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, Q1 (8 marks): A fair spinner has ten sectors, labelled 1, 2, …, 10. In order to start a game, Kofi has to obtain an 8, 9 or 10 on the spinner. (a) Find the probability that K
- June 2023, Statistics Minor, Q3 (10 marks): A fair four-sided dice has its faces numbered 0, 1, 2, 3. The dice is rolled three times. The discrete random variable X is the sum of the lowest and highest sc
- 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, Q1 (12 marks): Ryan has 6 one-pound coins and 4 two-pound coins. Ryan decides to select 3 of these coins at random to donate to a charity. The total value, in pounds, of these
- June 2023, AS Statistics A, Q2 (6 marks): A group of friends live by the sea. Each day they look out to sea in the hope of seeing a dolphin. The probability that they see a dolphin on any day is 0.15. Y
- 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, Q4 (10 marks): At a parcel delivery company it is known that the probability that a parcel is delivered to the wrong address is 0.0005. On a particular day, 15 000 parcels are
- 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, Q1 (7 marks): During a meteor shower, the number of meteors that can be seen at a particular location can be modelled by a Poisson distribution with mean 1.2 per minute. (a)
- June 2022, Statistics Major, Q3 (6 marks): The table shows the probability distribution of the random variable X, where a and b are constants. r 0 1 2 3 4 a b b2 P(X = r) 0.24 0.32 (a) Given that E(X ) =
- 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, Q1 (6 marks): In a quiz a contestant is asked up to four questions. The contestant’s turn ends once the contestant gets a question wrong or has answered all four questions. T
- June 2022, Statistics Minor, Q4 (5 marks): Alex is practising bowling at a cricket wicket. Every time she bowls a ball, she has a 30% chance of hitting the wicket. (a) Assuming that successive bowls are
- 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, Q1 (6 marks): A fair five-sided spinner has sectors labelled 1, 2, 3, 4, 5. In a game at a stall at a charity event, the spinner is spun twice. The random variable X represen
- June 2022, AS Statistics A, Q2 (7 marks): On a car assembly line, a robot is used for a particular task. (a) State the conditions under which a Poisson distribution is an appropriate model for the numbe
- 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
- June 2022, AS Statistics A, Q7 (7 marks): On average one in five packets of a breakfast cereal contains a voucher for a discount on the next packet bought. Whether or not a packet contains a voucher is
- November 2021, Statistics Major, Q2 (13 marks): In a game at a charity fair, a player rolls 3 unbiased six-sided dice. The random variable X represents the difference between the highest and lowest scores. 1
- 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, Q4 (8 marks): A radioactive source contains 1 000 000 nuclei of a particular radioisotope. On average 1 in 200 000 of these nuclei will decay in a period of 1 second. The ran
- November 2021, Statistics Major, Q6 (14 marks): Cosmic rays passing through the upper atmosphere cause muons, and other types of particle, to be formed. Muons can be detected when they reach the surface of th
- 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, Q1 (7 marks): The probability distribution of a discrete random variable X is given by the formula ^ h for r = 1, 2, 3, 4, 5. 2 P ( X r ) k r ( 1 ) 1 = = - + 1 (a) Show that
- November 2021, Statistics Minor, Q5 (10 marks): Biological cell membranes have receptor molecules which perform various functions. It is known that the number of receptor molecules of a particular type can be
- 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, Q2 (10 marks): A football player is practising taking penalties. On each attempt the player has a 70% chance of scoring a goal. The random variable X represents the number of
- November 2021, AS Statistics A, Q4 (6 marks): It is known that in an electronic circuit, the number of electrons passing per nanosecond can be modelled by a Poisson distribution. In a particular electronic
- 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 A, Q7 (13 marks): A biologist is investigating migrating butterflies. Fig. 7.1 shows the numbers of migrating butterflies passing her location in 100 randomly chosen one-minute p
- 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, Q1 (9 marks): In a game at a fair, players choose 4 countries from a list of 10 countries. The names of all 10 countries are then put in a box and the player selects 4 of the
- November 2020, Statistics Major, Q2 (9 marks): On average 1 in 4000 people have a particular antigen in their blood (an antigen is a molecule which may cause an adverse reaction). (a) (i) A random sample of
- 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, Q1 (5 marks): A quiz team of 4 students is to be selected from a group of 7 girls and 5 boys. The team is selected at random from the students in the group. The number of gir
- November 2020, Statistics Minor, Q2 (11 marks): On computer monitor screens there are often one or more tiny dots which are permanently dark and do not display any of the image. Such dots are known as ‘dead p
- November 2020, Statistics Minor, Q4 (10 marks): Cards are drawn at random from a standard pack of 52 cards, one at a time, until one of the 4 aces is drawn. After each card is drawn, it is replaced in the pac
- 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, Q1 (12 marks): The random variable X represents the number of cars arriving at a car wash per 10-minute period. From observations over a number of days, an estimate was made o
- 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 Major, Q1 (11 marks): A fair six-sided dice is rolled three times. The random variable X represents the lowest of the three scores. The probability distribution of X is given by the
- June 2019, Statistics Major, Q2 (9 marks): A special railway coach detects faults in the railway track before they become dangerous. (a) Write down the conditions required for the numbers of faults in th
- 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, Q2 (9 marks): A market researcher wants to interview people who watched a particular television programme. Audience research data used by the broadcaster indicates that 12% o
- June 2019, Statistics Minor, Q4 (17 marks): Zara uses a metal detector to search for coins on a beach. She wonders if the numbers of coins that she finds in an area of 10m2 can be modelled by a Poisson di
- 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, Q1 (8 marks): The discrete random variable X has probability distribution defined by P(X = r) = k(r2 + 3r) for r = 1, 2, 3, 4, 5, where k is a constant. (a) Complete the tabl
- 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 2019, AS Statistics B, Q2 (8 marks): Leila and Caleb are playing a game, using fair six‑sided dice and unbiased coins. • Leila rolls two dice, and her score L is the total of the scores on the two
- June 2018, AS Statistics A, Q1 (7 marks): Over a period of time, radioactive substances decay into other substances. During this decay a Geiger counter can be used to detect the number of radioactive pa
- 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
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