AQA AS Level Mathematics Paper 2, June 2025: Question 14

1 mark · Easy difficulty · Short Answer

Given independent events A and B with P(A) = 0.25 and P(B) = 0.6, find the value of P(A ∩ B).

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Question

Question 14 states: 'The events A and B are independent. It is given that P(A) = 0.25 and P(B) = 0.6. Find the value of P(A ∩ B). Circle your answer.' The multiple choice options displayed horizontally below are 0, 0.15, 0.35, and 0.85. Total marks: 1.
Question text

14 The events A and B are independent.

It is given that P(A) = 0.25 and P(B) = 0.6

Find the value of P(A ∩ B)

Circle your answer.

[1 mark]

00.15 0.35 0.85

Mark scheme

Show the mark scheme Mark scheme for Question 14: Marking instructions state 'Circles the second answer', AO 1.1b, B1 mark, with typical solution '0.15'. Total for Question 14 is 1 mark.

Q Marking instructions AO Marks Typical solution

14 Circles the second answer 1.1b B1

0.15

Question 14 Total 1

How to answer it

Probability: Independent Events Multiplication Rule

What this question tests

This question tests your understanding of the formal definition and multiplication rule for independent events in statistics, specifically calculating the probability of the intersection P(A ∩ B) , and differentiating independent events from mutually exclusive events.

Question 14 • Multiple Choice • 1 Mark

Finding P(A ∩ B) for Independent Events

✅ Correct Answer

The correct option to circle is the second value:

0.15

Mark scheme: [B1] for circling 0.15 (AO 1.1b)

💡 Key Knowledge

  • Independence condition: Two events A and B are independent if and only if:
    P(A ∩ B) = P(A) × P(B)
  • Mutually exclusive condition: Events cannot occur at the same time:
    P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B)

📐 Step-by-Step Calculation

  1. State the rule:
    Since A and B are independent:
    P(A ∩ B) = P(A) × P(B)
  2. Substitute given values:
    P(A) = 0.25
    P(B) = 0.6
  3. Multiply:
    P(A ∩ B) = 0.25 × 0.6 = 0.15
    Tip: 0.25 = 1/4, and (1/4) of 0.6 = 0.15

❌ Common Traps in the Given Distractors

  • Choosing 0: Conflating independent with mutually exclusive. If events were mutually exclusive, P(A ∩ B) = 0 .
  • Choosing 0.85: Adding the probabilities instead of multiplying: 0.25 + 0.6 = 0.85 . This represents P(A) + P(B) , not intersection.
  • Choosing 0.35: Subtracting probabilities: 0.6 - 0.25 = 0.35 .

🧠 Exam Technique & Examiner Insight

  • Look out for trigger words: The word "independent" is an explicit instruction to use the product rule P(A ∩ B) = P(A) × P(B) .
  • One clear circle: In 1-mark multiple choice questions, ensure your chosen answer is unambiguously circled. If you change your mind, cross out your initial choice completely and circle the intended one clearly.

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.