Probability — AS & A Level Mathematics (9709) questions by topic
Working with conditional probability across two bags of coloured marbles combined with a fair dice roll, modelling a driver's route choice at a junction from given percentages, and tracking rain probability across four consecutive days where each day depends on the last are typical of the 18 probability questions from 2023 to 2025, worth 5 to 9 marks.
Find, draw, show and determine are the command words tracked here, with draw expected for a tree diagram before probabilities are combined. Because a tree diagram with dependent branches is easy to set up incorrectly, submit your working for instant marking, so a wrongly conditioned branch or a missed multiplication across sequential days is caught before it changes every probability that follows.
May–June 2025, Paper 51
A bag contains 10 marbles, of which 4 are red and 6 are blue. Four marbles are selected from the bag at random, without replacement. The random variable X denotes the number of…
Answer this question and get it marked →May–June 2025, Paper 52
A bag contains 4 blue marbles and 12 red marbles. One marble is selected at random from the bag. If this marble is blue, it is replaced in the bag, but if it is red, it is not…
Answer this question and get it marked →Vehicles approaching a certain road junction from Bromley must go either left, right or straight on. Over time, it is known that 30% turn left, 25% turn right and 45% go straight…
Answer this question and get it marked →May–June 2025, Paper 53
Bag A contains 6 red marbles, 5 blue marbles and 1 green marble. Bag B contains 5 red marbles and 3 blue marbles. A marble is chosen at random from bag A and placed in bag B. A…
Answer this question and get it marked →May–June 2025, Paper 55
Students applying to Drydale College take an entrance test. A student is either accepted or rejected or required to take another test with probabilities 0.3, 0.2 and 0.5…
Answer this question and get it marked →May–June 2024, Paper 51
A game for two players is played using a fair 4-sided dice with sides numbered 1, 2, 3 and 4. One turn consists of throwing the dice repeatedly up to a maximum of three times.…
Answer this question and get it marked →Harry has three coins: - One coin is biased so that the probability of obtaining a head when it is thrown is 1/3. - The second coin is biased so that the probability of obtaining…
Answer this question and get it marked →May–June 2024, Paper 52
Seva has a coin which is biased so that when it is thrown the probability of obtaining a head is 1/3. He also has a bag containing 4 red marbles and 5 blue marbles. Seva throws…
Answer this question and get it marked →May–June 2024, Paper 53
Box A contains 6 green balls and 3 yellow balls. Box B contains 4 green balls and x yellow balls. A ball is chosen at random from box A and placed in box B. A ball is then chosen…
Answer this question and get it marked →October–November 2024, Paper 51
Rahul has two bags, X and Y. Bag X contains 4 red marbles and 2 blue marbles. Bag Y contains 3 red marbles and 4 blue marbles. Rahul also has a coin which is biased so that the…
Answer this question and get it marked →October–November 2024, Paper 52
At a college, the students choose exactly one of tennis, hockey or netball to play. The numbers of students in Year 1 and Year 2 playing each sport are: Tennis Hockey Netball…
Answer this question and get it marked →October–November 2024, Paper 53
30% of the residents of Wimfield own an electric car. Three residents are chosen at random. Find the probability that either all three own an electric car or none of them owns an…
Answer this question and get it marked →May–June 2023, Paper 51
A children's wildlife magazine is published every Monday. For the next 12 weeks it will include a model animal as a free gift. There are five different models: tiger, leopard,…
Answer this question and get it marked →May–June 2023, Paper 52
A sports event is taking place for 4 days, beginning on Sunday. The probability that it will rain on Sunday is 0.4. On any subsequent day, the probability that it will rain is 0.7…
Answer this question and get it marked →May–June 2023, Paper 53
Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events A and B are defined as follows. A: The sum of the two…
Answer this question and get it marked →October–November 2023, Paper 51
A red spinner has four sides labelled 1, 2, 3, 4. When the spinner is spun, the score is the number on the side on which it lands. The random variable X denotes this score. The…
Answer this question and get it marked →October–November 2023, Paper 52
Freddie has two bags of marbles. Bag X contains 7 red marbles and 3 blue marbles. Bag Y contains 4 red marbles and 1 blue marble. Freddie chooses one of the bags at random. A…
Answer this question and get it marked →October–November 2023, Paper 53
Tim has two bags of marbles, A and B. Bag A contains 8 white, 4 red and 3 yellow marbles. Bag B contains 6 white, 7 red and 2 yellow marbles. Tim also has an ordinary fair 6-sided…
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)