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mutually exclusive events

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: mutually exclusive events

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about mutually exclusive events. Then check against the key terms: key terms from mutually exclusive events. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: key terms from mutually exclusive events.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: mutually exclusive events. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Mathematics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: A dice is rolled. Are "rolling an even number" and "rolling a 6" mutually exclusive?

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about mutually exclusive events.

Lesson 2: Core Concepts: mutually exclusive events

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on mutually exclusive events. Check them against the notes below.

Main Content (35 minutes)

Definition: Two events are mutually exclusive if they cannot happen at the same time. If one happens, the other cannot.
TermMeaningExample
Mutually ExclusiveCannot occur togetherRolling 3 AND rolling 5 on same dice roll
ExhaustiveEvents cover all possible outcomesHeads or Tails covers all coin outcomes
P(A or B)Probability of A or B happeningP(Heads or Tails) = 1

Practice (10 minutes)

Q: A dice is rolled. Are "rolling an even number" and "rolling a 6" mutually exclusive?

Answer: NO - 6 is an even number, so both can happen together

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: mutually exclusive events

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: key terms from mutually exclusive events. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Q1: A dice is rolled. Are "rolling an even number" and "rolling a 6" mutually exclusive?

Answer: NO - 6 is an even number, so both can happen together

Q2: A bag has 5 red, 3 blue and 2 yellow balls. Find P(red or yellow).

Answer: P(red or yellow) = 5/10 + 2/10 = 7/10 (or count: 7 balls out of 10)

Q3: P(A) = 0.4, P(B) = 0.35. If A and B are mutually exclusive, find P(A or B).

Answer: P(A or B) = 0.4 + 0.35 = 0.75

Q4: A spinner has outcomes: A, B, C, D. P(A) = 0.3, P(B) = 0.25, P(C) = 0.2. Find P(D).

Answer: P(D) = 1 - (0.3 + 0.25 + 0.2) = 1 - 0.75 = 0.25

Q5: In a survey: 40 people like tea, 35 like coffee, 15 like both. Total surveyed = 60. How many like neither?

Answer: Tea or Coffee = 40 + 35 - 15 = 60. So 60 - 60 = 0 like neither

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: mutually exclusive events

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Extended Answer 6 marks: A dice is rolled. Let A = "even number" and B = "number greater than 4". (a) Are A and B mutually exclusive? Justify your answer. (b) Find P(A), P(B), and P(A ∩ B). (c) Use the formula P(A ∪ B) = P(A) + P(B) − P(A ∩ B) to find P(A or B). <div class="

(a) No — 6 is both even AND greater than 4, so they can happen together. (b) A = {2,4,6}, so P(A) = 3/6 = 1/2. B = {5,6}, so P(B) = 2/6 = 1/3. A ∩ B = {6}, so P(A ∩ B) = 1/6. (c) P(A ∪ B) = 1/2 + 1/3 − 1/6 = 3/6 + 2/6 − 1/6 = 4/6 = 2/3. Check: A ∪ B = {2,4,5,6} → 4 out of 6 = 2/3 ✓ Mark scheme: M1 for identifying 6 in both, A1 for "not mutually exclusive" with reason, M1 for correct P(A) and P(B), A1 for P(A ∩ B) = 1/6, M1 for applying formula, A1 for final answer 2/3

Exam Tips: Always check if events are mutually exclusive before adding probabilities | If events share outcomes, they are NOT mutually exclusive | Use P(not A) = 1 - P(A) when you need the complement | Check your answer makes sense - probabilities can't exceed 1 | "Or" means add for mutually exclusive events
Common Errors: Watch Out! 1. Wrong: Adding P(A) and P(B) when events are NOT mutually exclusive, getting P(A or B) > 1 Correct: If events overlap, use P(A or B) = P(A) + P(B) − P(A and B) to avoid double-counting 2. Wrong: Confusing mutually exclusive with independent — saying events can't be both Correct: Mutually exclusive means they can't happen together; independent means one doesn't affect the other. They are different concepts. 3. Wrong: Forgetting that P(A) + P(A') = 1, so P(A') = 1 − P(A) Correct: The complement rule always works — use it when "not A" is easier to find than A directly
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A survey of 200 people found: 90 like tea, 80 like coffee, 35 like both. (a) Are "liking tea" and "liking coffee" mutually exclusive? How do you know? (b) Find the probability that a randomly chosen person likes neither drink. (c) Josh says "Since 90 + 80 = 170, and 170 Answers: (a) No — 35 people like both, so they can happen together. (b) Tea or coffee = 90 + 80 − 35 = 135. Neither = 200 − 135 = 65. P(neither) = 65/200 = 0.325. (c) Josh is wrong. The fact that 90 + 80
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how mutually exclusive events connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of mutually exclusive events
  • Critical: "What are the limitations of the models used in mutually exclusive events?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)