AQA GCSE Mathematics Paper 2 (Higher), June 2025: Question 7

3 marks · Easy difficulty · Multi-step Problem

Given the probabilities of outcomes A and B for a set of mutually exclusive and exhaustive outcomes, with conditions P(C) = P(B) + 0.1 and P(D) = P(E), work out P(D).

Practise this question

Question

Question 7 shows a probability table for five mutually exclusive and exhaustive outcomes: A, B, C, D, and E. The probability of A is 0.18, the probability of B is 0.2, and C, D, and E are blank. Below the table, it is stated that P(C) = P(B) + 0.1 and P(D) = P(E). The prompt asks to work out P(D) for 3 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 7: M1 for finding P(C) as 0.2 + 0.1 = 0.3; M1 for subtracting probabilities from 1 to find the sum of D and E, shown as 1 - 0.18 - 0.2 - their P(C) or 0.32; A1 for the correct answer 0.16 (or equivalent fraction, decimal, or percentage).

How to answer it

Calculating Unknown Probabilities from Exhaustive Events

📋 What this question tests

This question assesses your ability to:

  • Apply the fundamental rule that the sum of probabilities for all mutually exclusive, exhaustive outcomes is equal to 1.
  • Interpret and calculate linked probabilities from conditional statements (e.g. P(C) = P(B) + 0.1 ).
  • Use basic algebraic reasoning to divide remaining probabilities equally between two identical outcomes ( P(D) = P(E) ).
Question 7 • 3 Marks

Problem Breakdown & Step-by-Step Solution

Find the value of P(D) given the table and conditions

Outcome A B C D E
Probability 0.18 0.2 P(B) + 0.1 P(E) P(D)

📐 Step-by-Step Calculation

  1. Find P(C):
    P(C) = P(B) + 0.1 = 0.2 + 0.1 = 0.3
  2. Find the total of known outcomes (A, B, C):
    P(A) + P(B) + P(C) = 0.18 + 0.2 + 0.3 = 0.68
  3. Find the remaining probability for D and E:
    Since total probability = 1:
    P(D) + P(E) = 1 - 0.68 = 0.32
  4. Calculate P(D):
    Since P(D) = P(E) , divide the remainder equally by 2:
    P(D) = 0.32 ÷ 2 = 0.16

✅ Correct Answer & Marks Breakdown

  • Final Answer: 0.16 (or equivalent fraction 4/25 , or 16% )
  • [M1] For calculating P(C) : 0.2 + 0.1 or 0.3 .
  • [M1] For subtracting known values from 1:
    1 - 0.18 - 0.2 - 0.3 = 0.32 .
  • [A1] For final correct answer: 0.16 .

Examiner Advice & Key Tips

💡 Key Knowledge

  • Total Probability Rule: All possible mutually exclusive outcomes must add up to exactly 1 .
  • Writing on the paper: You are allowed to write probabilities directly into the blank spaces in the table to help organize your working.
  • Equivalent forms: Answers can be given as decimals, fractions, or percentages unless specified otherwise.

❌ Common Errors

  • Stopping at 0.32: Forgetting that 0.32 is the combined sum of both D and E , not the final answer for P(D) .
  • Place Value Slips: Adding 0.2 + 0.1 and mistakenly treating decimals inconsistently, or writing 0.18 + 0.2 = 0.20 instead of 0.38 .
  • Misreading the condition: Confusing P(B) + 0.1 with P(A) + 0.1 .

🧠 Exam Technique

  • Show each line of working: Even if you make an arithmetic error when adding probabilities, showing the method 1 - (sum of probabilities) can still earn a method mark (M1).
  • Sanity Check: Always check that your final probabilities 0.18 + 0.2 + 0.3 + 0.16 + 0.16 sum to exactly 1 .

Topics

Probability · 3.5 Probability

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.