AQA AS Level Mathematics Paper 2, June 2025: Question 13

1 mark · Easy difficulty · Short Answer

Find the probability from a two-way table that a randomly chosen student is a Year 12 student whose favourite sport is netball.

Practise this question

Question

Question 13 displays a two-way frequency table showing students' favourite sport (football, rugby, netball, tennis, Total) across Year 12 and Year 13. Year 12 entries are 57 for football, 30 for rugby, 36 for netball, 2 for tennis, and 125 total. Year 13 entries are 33 for football, 11 for rugby, 19 for netball, 12 for tennis, and 75 total. The column totals are 90, 41, 55, 14, with an overall total of 200 students. Below the table, it asks: 'Find the probability that the student chosen is a year 12 student whose favourite sport is netball. Circle your answer.' The choices are 0.18, 0.275, 0.288, and 0.44.
Question text

13 The table shows the favourite sport of a group of students from years 12 and 13.

football rugby netball tennis Total

Year 12 57 30 36 2 125

Year 13 33 11 19 12 75

Total 90 41 55 14 200

A student is chosen at random.

Find the probability that the student chosen is a year 12 student whose favourite sport

is netball.

Circle your answer.

[1 mark]

0.18 0.275 0.288 0.44

Mark scheme

Show the mark scheme Mark scheme table for Question 13 shows Marking instructions: 'Circles the first answer', AO: 1.1b, Marks: B1, and Typical solution: '0.18'.

Q Marking instructions AO Marks Typical solution

13 Circles the first answer 1.1b B1

0.18

Question 13 Total 1

How to answer it

Two-Way Tables & Joint Probability

📋 What this question tests

This question tests your ability to extract joint frequencies from a contingency table (two-way table) and calculate simple unconditional probabilities across an entire sampled population.

Question 13 Walkthrough

AQA AS Mathematics • Statistics • 1 Mark (Multiple Choice)

football rugby netball tennis Total
Year 12 57 30 36 2 125
Year 13 33 11 19 12 75
Total 90 41 55 14 200

✅ Correct Answer

0.18

Mark Scheme: Circles the first answer ( 0.18 ) • [B1] (AO 1.1b)

💡 Key Knowledge

  • Joint Probability P(A ∩ B): The probability that both event A and event B occur simultaneously.
  • Total Sample Space: The question states "A student is chosen at random" from the whole group, meaning the denominator is the grand total: n(S) = 200 .
  • Intersection: The number of students who are both Year 12 and prefer netball is the value at the intersection of the Year 12 row and Netball column.

📐 Step-by-Step Calculation

  1. Identify the intersection count:
    Look across the Year 12 row and down the netball column:
    n(Year 12 ∩ Netball) = 36
  2. Identify the total sample size:
    Look at the bottom-right grand total:
    n(Total) = 200
  3. Calculate the probability:
    P(Year 12 ∩ Netball) = 36 / 200
  4. Convert to decimal:
    36 / 200 = 18 / 100 = 0.18

❌ Common Errors & Distractor Traps

  • 0.288 (Conditional Trap): Calculating 36 / 125 = 0.288 . This finds P(Netball | Year 12), which is only valid if the student was chosen from Year 12 only.
  • 0.275 (Marginal Trap): Calculating 55 / 200 = 0.275 . This gives the probability of choosing any netball player, forgetting the Year 12 condition.
  • 0.44: Calculating 11 / 25 or other incorrect column-row ratios.

🧠 Exam Technique & Examiner Commentary

  • Check the phrasing carefully: Always look at the opening sentence. "A student is chosen at random" without qualifier means the denominator is always the overall total (200).
  • Distinguish "AND" vs "GIVEN": "A Year 12 student whose favourite sport is netball" represents an intersection ( ∩ ). It is not a conditional statement like "Given that the student is in Year 12...".
  • Quick Elimination: Because 200 has a factor of 100, 36 / 200 immediately halves to 18 / 100 , which is readily identifiable as 0.18 in under 10 seconds.

Topics

Statistics · M: Probability

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