Probability, Venn and tree diagrams: WJEC A‑Level Maths questions

WJEC A-Level Maths past-paper questions on 3.1 Probability, Venn and tree diagrams, 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 16 questions on Probability, Venn and tree diagrams, as a list

Summer 2025, Unit 4, Q2 (12 marks): 2. Selina is sitting two multiple-choice tests. (a) For each question in the first test, she classifies herself as ‘very confident’, ‘confident’ or ‘not confide
Summer 2025, AS Unit 2, Q4 (8 marks): 4. The following Venn diagram shows the events A, B, C, D together with some probabilities. C p A B 0·13 0·08 0·17 q D r (a) Find: (i) P(A) (ii) P(A ∩ B). [2] (
Summer 2024, Unit 4, Q4 (21 marks): 4. Jake works for a parcel delivery company. The masses, in kilograms, of parcels he delivers are normally distributed with mean 2.2 and standard deviation 0.3.
Summer 2024, AS Unit 2, Q3 (8 marks): 3. The following Venn diagram shows the participation of 100 students in three activities, A, B, and C, which represent athletics, baseball and climbing respect
Summer 2023, Unit 4, Q1 (6 marks): 1 Two fair, non-cubical dice give scores of 1 to 4 and 1 to 8 respectively. A dice is selected at random and then rolled once. a) Find the probability that the
Summer 2023, Unit 4, Q2 (7 marks): A certain fungus occurs in a population of trees in two mutually exclusive types, 0 2 X and Y. It is known that 4% of the trees have type X of the fungus and th
Summer 2023, AS Unit 2, Q1 (10 marks): The events A and B are such that P(A) = 0.3, P(B) = 0.2 and P(A ∩ B) = 0.1. 0 1 a) Find P(A ∪ B). [2] The event C is such that P(C) = 0.45. The events B and C a
Summer 2023, AS Unit 2, Q3 (4 marks): 3 The probability distribution of a discrete random variable X is given below. x 4 8 16 0.3 0.5 0.2 P(X = x) Two independent values of X are generated. Find the
Summer 2022, Unit 4, Q2 (8 marks): 2 System faults that occur in a particular type of aeroplane can be categorised in one of three mutually exclusive ways as compass (event C), gyroscopic (event
Summer 2022, AS Unit 2, Q1 (7 marks): 1 The events A and B are such that ∪ P(A) = 0·3, P(B) = 0·6, P(A B) = 0·82. a) Determine whether or not A and B are independent. [4] b) Find the probability tha
Summer 2019, Unit 4, Q1 (5 marks): 1 Val buys electrical components from one of 3 suppliers A, B, C, in the ratio 2 : 1 : 7. The probability that the component is faulty is 0.33 for A, 0.45 for B
Summer 2019, Unit 4, Q2 (10 marks): 2 Four children are playing a game in order to win a calculator. They take turns, starting with Alex, followed by Ben, then Caroline, then Danielle, rolling a f
Summer 2019, AS Unit 2, Q1 (7 marks): 1 3 5 0 1 Three events A, B, C are such that P(B) = , P(C) = , P(A ∪ B) = , P(A ∪ C) = . 5 6 4 6 The events A and B are independent. a) Find P(A). [3] b) Determ
Summer 2018, Unit 4, Q1 (7 marks): 1 An architect bids for two construction projects. He estimates the probability of winning bid A is 0.6, the probability of winning bid B is 0.5 and the probabi
Summer 2018, Unit 4, Q2 (7 marks): a) Marie is an athlete who competes in the high jump. In a certain competition she 0 2 is allowed two attempts to clear each height, but if she is successful wi
Summer 2018, AS Unit 2, Q2 (7 marks): 2 The Venn diagram shows the subjects studied by 40 sixth form students. F represents the set of students who study French, M represents the set of students who

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