plumiDiscrete distributions: Edexcel A‑Level Further Maths questions
Every Edexcel 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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All 37 questions on Discrete 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, Q2 (9 marks): The discrete random variable X has probability distribution x –1 a b P(X = x) 1 2 1 4 1 4 where a and b are positive constants. (a) Find an expression for E(X)
- June 2025, Further Statistics 1, Q5 (10 marks): A football team scores goals at an average rate of 1.8 goals per match. (a) Give two assumptions that would be necessary to use a Poisson distribution to model
- 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 2025, AS Further Statistics 1, Q2 (12 marks): The discrete random variable X represents the score when a spinner is spun. The probability distribution of X is given by x 2 5 9 P(X = x) 0.6 0.3 0.1 (a) Find
- June 2025, AS Further Statistics 1, Q3 (11 marks): Raoul, Steffi and Taro are catching butterflies for research. The number of butterflies caught by Raoul per hour may be assumed to follow a Poisson distribution
- June 2024, Further Statistics 1, Q1 (6 marks): The discrete random variable X has the following probability distribution x – 1 0 1 3 5 P(X = x) 0.2 0.1 0.2 0.25 0.25 (a) Find Var(X ) (3) (b) Find Var(X 2) (3
- 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, 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 2024, AS Further Statistics 1, Q2 (13 marks): A manager keeps a record of accidents in a canteen. Accidents occur randomly with an average of 2.7 per month. The manager decides to model the number of accide
- June 2024, AS Further Statistics 1, Q3 (6 marks): The discrete random variable X has probability distribution, x –1 0 1 3 7 P(X = x) p r p 0.3 r where p and r are probabilities. Given that E(X) = 1.95 find the
- June 2023, Further Statistics 1, Q1 (9 marks): The discrete random variable X has probability distribution x – 2 – 1 0 1 3 P(X = x) 0.25 a b a 0.30 where a and b are probabilities. (a) Find E(X) (2) Given th
- 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 2023, AS Further Statistics 1, Q1 (6 marks): The discrete random variable X has the following distribution x 0 1 2 3 4 P(X = x) r k k 2 k 3 k 4 where r and k are positive constants. The standard deviation
- June 2023, AS Further Statistics 1, Q3 (16 marks): A machine produces cloth. Faults occur randomly in the cloth at a rate of 0.4 per square metre. The machine is used to produce tablecloths, each of area A squar
- June 2022, Further Statistics 1, Q2 (9 marks): The discrete random variable X has probability distribution x –5 –1 0 5 b P(X = x) 0.3 0.25 0.1 0.15 0.2 where b is a constant and b > 5 (a) Find E(X ) in terms
- June 2022, Further Statistics 1, Q3 (14 marks): During the summer, mountain rescue team A receives calls for help randomly with a rate of 0.4 per day. (a) Find the probability that during the summer, mountain
- 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, AS Further Statistics 1, Q2 (10 marks): Xena catches fish at random, at a constant rate of 0.6 per hour. (a) Find the probability that Xena catches exactly 4 fish in a 5‑hour period. (2) The probabili
- June 2022, AS Further Statistics 1, Q4 (14 marks): The discrete random variable X has the following probability distribution x 0 2 3 6 P(X = x) p 0.25 q 0.4 (a) Find in terms of q (i) E(X ) (ii) E(X 2) (2) Given
- November 2021, Further Statistics 1, Q2 (14 marks): On a weekday, a garage receives telephone calls randomly, at a mean rate of 1.25 per 10 minutes. (a) Show that the probability that on a weekday at least 2 call
- November 2021, Further Statistics 1, Q4 (10 marks): Members of a photographic group may enter a maximum of 5 photographs into a members only competition. Past experience has shown that the number of photographs,
- 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, Q1 (13 marks): The number of customers entering Jeff’s supermarket each morning follows a Poisson distribution. Past information shows that customers enter at an average rate
- November 2020, Further Statistics 1, Q2 (4 marks): The discrete random variables W, X and Y are distributed as follows W ~ B(10, 0.4) X ~ Po(4) Y ~ Po(3) (a) Explain whether or not Po(4) would be a good approxim
- 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.
- November 2020, Further Statistics 1, Q4 (8 marks): The discrete random variable X has the following probability distribution. x –5 –2 3 4 P(X = x) 1 12 1 6 1 4 1 2 (a) Find Var(X) (3) The discrete random variabl
- November 2020, AS Further Statistics 1, Q1 (10 marks): A plumbing company receives call-outs during the working day at an average rate of 2.4 per hour. (a) Find the probability that the company receives exactly 7 ca
- November 2020, AS Further Statistics 1, Q3 (7 marks): The probability distribution of the discrete random variable X is P(X = x) = k x x m x x for = 1, 2 and 3 for = 6 and 9 2 0 otherwise where k a
- November 2020, AS Further Statistics 1, Q4 (8 marks): During the morning, the number of cyclists passing a particular point on a cycle path in a 10-minute interval travelling eastbound can be modelled by a Poisson
- 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, Q2 (8 marks): Indre works on reception in an office and deals with all the telephone calls that arrive. Calls arrive randomly and, in a 4-hour morning shift, there are on ave
- 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
- June 2019, AS Further Statistics 1, Q3 (13 marks): Andreia’s secretary makes random errors in his work at an average rate of 1.7 errors every 100 words. (a) Find the probability that the secretary makes fewer th
- June 2019, AS Further Statistics 1, Q4 (14 marks): The discrete random variable X has probability distribution x –3 –1 1 2 4 P(X = x) q 7 30 7 30 q r where q and r are probabilities. (a) Write down, in terms of
- June 2018, AS Further Statistics 1, Q2 (11 marks): The number of heaters, H, bought during one day from Warmup supermarket can be modelled by a Poisson distribution with mean 0.7 (a) Calculate P(H 2) (1) The n
- June 2018, AS Further Statistics 1, Q3 (12 marks): A fair six-sided black die has faces numbered 1, 2, 2, 3, 3 and 4 The random variable B represents the score when the black die is rolled. (a) Write down the va
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