P6 Mathematics - Term I

Topic 1: Sets

Lesson 4: Probability Using Venn Diagrams

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

• Define probability in simple terms
• Calculate simple probabilities using Venn diagrams
• Find the probability of events using set notation
• Apply probability concepts to real-life situations
• Solve problems involving probabilities using Venn diagrams

Review: Venn Diagrams

From Lesson 3, we learned:

• Rectangle = Universal set (U)
• Circles = Sets (A, B)
• Union (∪) = A OR B (combine all)
• Intersection (∩) = A AND B (only common)

Today: We use Venn diagrams to calculate probabilities!

What is Probability?

Probability = How likely something is to happen

Examples:

• "Will it rain today?"
• "If I pick a ball from a bag, what color will it be?"
• "What are the chances of winning a game?"

Probability tells us the CHANCE of something happening

Probability Formula

Probability = Number of favorable outcomes
              Total number of possible outcomes

Short form:

P = Favorable
    Total

Probability is written as a fraction

Example: Simple Probability

A bag contains 10 balls:

• 6 red balls
• 4 blue balls

Question: What is the probability of picking a red ball?

P(red) = Number of red balls = 6  = 3
         Total balls          10   5

Probability Values

Important facts about probability:

• Probability of 0 = Impossible (will never happen)
• Probability of 1 = Certain (will definitely happen)
• All probabilities are between 0 and 1

Example:

P(red) = 3/5 = 0.6 (likely)
P(blue) = 2/5 = 0.4 (less likely)
P(red) + P(blue) = 3/5 + 2/5 = 5/5 = 1 ✓

Using Venn Diagrams for Probability

Venn diagrams help us:

• Count elements easily
• See relationships clearly
• Calculate probabilities accurately

Key: The diagram helps us COUNT what we need!

Example with Venn Diagram

Class of 40 learners:

• 25 like football
• 18 like netball
• 10 like both

Filling the Venn Diagram

Step 1: Start with intersection (both)

• Both sports: 10 learners

Step 2: Calculate "only" regions

• Football only: 25 - 10 = 15 learners
• Netball only: 18 - 10 = 8 learners

Step 3: Find "neither"

• Neither: 40 - (15 + 10 + 8) = 7 learners

Check: 15 + 10 + 8 + 7 = 40 ✓

Calculating Probabilities

Using our example (40 learners):

• Football only: 15
• Both sports: 10
• Netball only: 8
• Neither: 7

Questions:

• P(only football) = 15/40 = 3/8
• P(only netball) = 8/40 = 1/5
• P(both) = 10/40 = 1/4
• P(neither) = 7/40

Practice Problem

Survey of 50 learners about breakfast:

• 30 ate porridge (P)
• 25 ate bread (B)
• 12 ate both

Draw a Venn diagram and find:
a) P(only porridge)
b) P(only bread)
c) P(both)
d) P(neither)

Solution: Fill the Diagram

Step 1: Both = 12

Step 2: Calculate regions

• Porridge only: 30 - 12 = 18
• Bread only: 25 - 12 = 13
• Neither: 50 - (18 + 12 + 13) = 7

Check: 18 + 12 + 13 + 7 = 50 ✓

Solution: Probabilities

a) P(only porridge) = 18/50 = 9/25

b) P(only bread) = 13/50

c) P(both) = 12/50 = 6/25

d) P(neither) = 7/50

Check: All probabilities add to 1 (50/50) ✓

Real-Life Application

Weather forecast:

• P(rain tomorrow) = 0.7 = 70% chance
• P(no rain) = 0.3 = 30% chance

Sports:

• P(team wins) = 2/3
• P(team loses or draws) = 1/3

Venn diagrams help us organize information to find probabilities!

Key Steps for Probability Problems

1. Draw Venn diagram
2. Fill in numbers (start with intersection!)
3. Calculate other regions
4. Check: Total should equal U
5. Calculate probabilities (favorable/total)
6. Check: All probabilities should add to 1

Practice: Quick Problem

A box contains 24 pencils:

• 15 red pencils
• 12 blue pencils
• 3 pencils are both red and blue (striped)

Find:

• P(red only)
• P(blue only)
• P(striped)

Solution

Fill Venn diagram:

• Both (striped): 3
• Red only: 15 - 3 = 12
• Blue only: 12 - 3 = 9
• Check: 12 + 3 + 9 = 24 ✓

Probabilities:

• P(red only) = 12/24 = 1/2
• P(blue only) = 9/24 = 3/8
• P(striped) = 3/24 = 1/8

Summary

Probability:

• Shows how likely something is to happen
• Formula: P = favorable/total
• Always between 0 and 1
• All probabilities add up to 1

Venn diagrams:

• Help organize information
• Make counting easier
• Lead to accurate probability calculations

Review: Sets Topic Complete!

Lesson 1: Types of sets (equal, equivalent, unequal)

Lesson 2: Universal sets, complement sets, subsets

Lesson 3: Venn diagrams (union and intersection)

Lesson 4: Probability using Venn diagrams ✓

You've completed Topic 1: Sets!

Homework

1. Basic probability: A jar has 20 sweets (8 yellow, 7 red, 5 green). Find P(yellow), P(red), P(green).

2. Venn diagram problem: In a village of 60 households, 40 have chickens, 35 have goats, 20 have both. Draw Venn diagram and find probabilities.

3. Reflection: Write 2-3 sentences: "What is probability and when might you use it in daily life?"

Expected time: 30 minutes

Next Topic Preview

Next, we will study:
Topic 2: Whole Numbers (5 periods)

Topics include:

• Place value
• Ordering numbers
• Rounding numbers
• Number operations

Sets knowledge will help you throughout mathematics!

Credits

Created: November 21, 2025
Based on: NCDC P6 Mathematics Curriculum - Topic 1: Sets

Source: National Curriculum Development Centre (NCDC), Uganda

Available from: https://ncdc.go.ug/

End of Sets Topic - Well done!