plumiGeometric and negative binomial distributions: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 1.3 Geometric and negative binomial distributions, 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.
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All 14 questions on Geometric and negative binomial distributions, as a list
- 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, 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, 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, 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, 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, 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, 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 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
- 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, 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 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
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