Binomial and geometric distributions — AS & A Level Mathematics (9709) questions by topic
Testing whether support for a political party has genuinely decreased using a binomial model, finding the expected number of spins before a fair spinner lands on a given number, and modelling the number of goals scored against a fixed attempt probability are typical of the 20 binomial and geometric distribution questions from 2023 to 2025, worth 4 to 11 marks.
Find and calculate lead the command words, with test, state and show used to justify a distribution's parameters or a hypothesis conclusion. Because choosing between a binomial and a geometric model changes every subsequent calculation, submit your working for instant marking, so a wrongly chosen distribution or a miscounted number of trials is caught at the point it happens rather than after the whole probability is computed.
May–June 2025, Paper 53
At a large college, all students who study Science also study exactly one of Art or Drama or Music. 20% of these students study Art, 45% study Drama and 35% study Music. 3…
Answer this question and get it marked →A fair six-sided dice with faces labelled 1, 2, 3, 4, 5, 6 is thrown repeatedly until a 3 is obtained. The number of throws taken is denoted by the random variable X. Find P(X =…
Answer this question and get it marked →May–June 2025, Paper 62
Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, p, that it will show a six on one throw is less than 1/6. She throws the dice 30 times…
Answer this question and get it marked →May–June 2025, Paper 65
It is claimed that 28% of voters in a certain town support the Forward Now political party. A researcher suspects that the true figure is less than 28%. She interviews a random…
Answer this question and get it marked →May–June 2024, Paper 51
In a certain area in the Arctic the probability that it snows on any given day is 0.7, independent of all other days. Find the probability that in a week (7 days) it snows on at…
Answer this question and get it marked →May–June 2024, Paper 52
Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.3, independently of other years. Find the…
Answer this question and get it marked →The residents of Mahjing were asked to classify their local bus service: - 25% of residents classified their service as good. - 60% of residents classified their service as…
Answer this question and get it marked →May–June 2024, Paper 53
Salah decides to attempt the crossword puzzle in his newspaper each day. The probability that he will complete the puzzle on any given day is 0.65, independent of other days. Find…
Answer this question and get it marked →May–June 2024, Paper 61
Every July, as part of a research project, Rita collects data about sightings of a particular kind of bird. Each day in July she notes whether she sees this kind of bird or not,…
Answer this question and get it marked →May–June 2024, Paper 63
In this question you should not use an approximating distribution. At an election in Menham last year, 24% of voters supported the Today Party. A student wishes to test whether…
Answer this question and get it marked →October–November 2024, Paper 51
Nicola throws an ordinary fair six-sided dice. The random variable X is the number of throws that she takes to obtain a 6. Find P(X < 8).
Answer this question and get it marked →October–November 2024, Paper 52
In a game, players attempt to score a goal by kicking a ball into a net. The probability that Leno scores a goal is 0.4 on any attempt, independently of all other attempts. The…
Answer this question and get it marked →October–November 2024, Paper 53
A factory produces chocolates. 30% of the chocolates are wrapped in gold foil, 25% are wrapped in red foil and the remainder are unwrapped. Indigo chooses 8 chocolates at random…
Answer this question and get it marked →May–June 2023, Paper 51
Eli has four fair 4-sided dice with sides labelled 1, 2, 3, 4. He throws all four dice at the same time. The random variable X denotes the number of 2s obtained. Show that P(X =…
Answer this question and get it marked →May–June 2023, Paper 52
A fair 5-sided spinner has sides labelled 1, 2, 3, 4, 5. The spinner is spun repeatedly until a 2 is obtained on the side on which the spinner lands. The random variable X denotes…
Answer this question and get it marked →May–June 2023, Paper 53
Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable X. State the value of E(X).
Answer this question and get it marked →May–June 2023, Paper 62
When a child completes an online exercise called a Mathlit, they might be awarded a medal. The publishers claim that the probability that a randomly chosen child who completes a…
Answer this question and get it marked →October–November 2023, Paper 51
Hazeem repeatedly throws two ordinary fair 6-sided dice at the same time. On each occasion, the score is the sum of the two numbers that she obtains. Find the probability that it…
Answer this question and get it marked →October–November 2023, Paper 52
George has a fair 5-sided spinner with sides labelled 1, 2, 3, 4, 5. He spins the spinner and notes the number on the side on which the spinner lands. Find the probability that it…
Answer this question and get it marked →October–November 2023, Paper 53
The probability that a driver passes an advanced driving test is 0.3 on any given attempt. Dipak keeps taking the test until he passes. The random variable X denotes the number of…
Answer this question and get it marked →Other AS & A Level Mathematics topics
- Differentiation (95)
- Algebra, logarithmic and exponential functions (87)
- Trigonometry (57)
- Series (37)
- Integration (33)
- Kinematics (33)
- The normal distribution (32)
- Energy, work and power (31)
- The Poisson distribution (31)
- Complex numbers (28)
- Sampling and estimation (28)
- Permutations and combinations (27)