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

Edexcel 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 14 questions on Geometric and negative binomial distributions, as a list

June 2025, Further Statistics 1, Q1 (7 marks): Irina is practising her serves in badminton and counts the number of her serves that are faults. She finds that 15% of her serves are faults. Assuming that each
June 2025, Further Statistics 1, Q6 (13 marks): A biased coin and a fair coin are thrown repeatedly. The probability that the biased coin shows heads is 1 3 Let B represent the number of throws of the biased
June 2024, Further Statistics 1, Q4 (12 marks): Every morning Geethaka repeatedly rolls a fair, six‑sided die until he rolls a 3 and then he stops. The random variable X represents the number of times he roll
June 2024, Further Statistics 1, Q6 (16 marks): The random variable X has probability generating function GX(t) where GX(t) = 1 4 3 −t (a) Use calculus to find Var(X ) Show your working clearly. (6) (b) Find
June 2024, Further Statistics 1, Q7 (18 marks): The probability of winning a prize when playing a single game of Pento is 1 5 When more than one game is played the games are independent. Sam plays 20 games. (
June 2023, Further Statistics 1, Q4 (6 marks): There are 32 students in a class. Each student rolls a fair die repeatedly, stopping when their total number of sixes is 4 Each student records the total number
June 2023, Further Statistics 1, Q6 (13 marks): The discrete random variable X has probability generating function G X t t t ( ) 2 2 3 2 (a) Specify the distribution of X (2) A fair die is rolled repeatedly.
June 2023, Further Statistics 1, Q7 (13 marks): Each time a spinner is spun, the probability that it lands on red is 0.2 (a) Find the probability that the spinner lands on red (i) for the 1st time on the 4th
June 2022, Further Statistics 1, Q4 (13 marks): In a game a spinner is spun repeatedly. When the spinner is spun, the probability of it landing on blue is 0.11 (a) Find the probability that the spinner lands
June 2022, Further Statistics 1, Q5 (5 marks): A random sample of 150 observations is taken from a geometric distribution with parameter 0.3 Estimate the probability that the mean of the sample is less than
November 2021, Further Statistics 1, Q5 (18 marks): Asha, Davinda and Jerry each have a bag containing a large number of counters, some of which are white and the rest are red. Each person draws counters from the
November 2020, Further Statistics 1, Q3 (9 marks): Suzanne and Jon are playing a game. They put 4 red counters and 1 blue counter in a bag. Suzanne reaches into the bag and selects one of the counters at random.
June 2019, Further Statistics 1, Q1 (6 marks): A chocolate manufacturer places special tokens in 2% of the bars it produces so that each bar contains at most one token. Anyone who collects 3 of these tokens
June 2019, Further Statistics 1, Q7 (12 marks): A spinner can land on red or blue. When the spinner is spun, there is a probability of 1 3 that it lands on blue. The spinner is spun repeatedly. The random var

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