Geometric and negative binomial distributions: OCR MEI A‑Level Further Maths questions

OCR MEI 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.

All 20 questions on Geometric and negative binomial distributions, as a list

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 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, 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 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, 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 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 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, 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 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 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, 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, 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 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, 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 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 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, 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
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 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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