DSE Maths: Probability — Tutor Lesson Plan (classical, mutually exclusive, independent)

2026-10-27

Tutor lesson-prep guides · Secondary maths

Nine out of ten probability errors come from adding when they should multiply. One rule decides it: separate routes add, consecutive steps multiply.

Objectives — the student can compute classical probability, identify mutually exclusive events and add, and identify independent events and multiply.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Fractions	Simplify 6/36	1/6
Counting	How many outcomes for two dice?	36
Complement	What does 1 – P(A) mean?	Probability A does not happen

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Classical probability	Favourable over total	Three questions
10-24 min	Mutually exclusive	Cannot happen together, so add	Two questions
24-40 min	Independent	No influence, so multiply	Two questions
40-50 min	Complements	At least once is one minus none	Two questions
50-57 min	Format	Write the sample space first	Rewrite one
57-60 min	Exit check	Three questions marked	Finish alone

03 Teaching script (read it out)

Scene 1: Write the sample space before counting

Two dice give 36 equally likely outcomes; a total of seven comes from six of them.
So the probability is 6/36, which simplifies to 1/6.
A clear sample space prevents missed cases.

Student lists the outcomes giving a total of five: four of them.

Scene 2: Exclusive events add, independent events multiply

Drawing a heart or a spade cannot happen together, so add to get 1/2.
Two heads in a row are independent, so multiply to get 1/4.
Test: can they happen at the same time? If yes, they are not exclusive.

Student judges red and a face card: not exclusive.

Scene 3: At least once is easiest by complement

At least one head in three tosses is one minus all tails, so 1 – 1/8 = 7/8.
Adding directly double counts.

Note: when you see at least, think complement.

04 Question types and worked steps

Type	Example	Steps	Answer
Classical	two dice total seven	6 over 36	1/6
Exclusive addition	heart or spade	13/52 plus 13/52	1/2
Independent product	two heads	Half times half	1/4
At least once	three tosses	One minus one eighth	7/8

Sanity check (teach this): All probabilities must sum to one; a total above one means something was counted twice.

05 Independent practice (3 questions)

Question	Answer	What to watch
Two dice total five	1/9	4 over 36
A red face card	3/26	6 over 52
At least one tail in four tosses	15/16	One minus one sixteenth

06 Common mistakes and what to say

Mistake	Student writes	Say this
Exclusive and independent mixed	multiplies exclusive events	Test whether both can happen.
Missing outcomes	counts three ways to total seven	Count ordered pairs.
Adding for at least	double counts	Use the complement.
Not simplified	leaves 6/36	Simplify to 1/6.

07 Homework (paper, section and question numbers)

Secondary maths chapter index — Use the three questions on this page

08 Exit check (last 5 minutes)

Question	Answer	Decision
Two dice total five	1/9	All right: move to statistics
A red face card	3/26	One wrong: re-teach sample space
At least one tail in four tosses	15/16	Two wrong: repeat scene 3

09 Tutor FAQ

Tree diagrams?

Best for multi-step experiments.

With or without replacement?

Without replacement, the denominator drops by one.

Link to statistics?

Probability is theory; statistics estimates from data.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.