P6 Mathematics - Term I

Topic 1: Sets

Lesson 4: Probability Using Venn Diagrams

Duration: 45 minutes

Today's Learning Objectives on Probability

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

Recalling Venn Diagrams from Lesson 3

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 Exactly Does Probability Measure?

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

The Probability Formula to Remember

Probability = Number of favorable outcomes
              Total number of possible outcomes

Short form:

P = Favorable
    Total

Probability is written as a fraction

Example: A Simple Probability Problem

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 Always Falls Between 0 and 1

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

P(red) + P(blue) = 3/5 + 2/5 = 5/5 = 1

Venn Diagrams Help Us Calculate Probability

Venn diagrams help us:

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

Key: The diagram helps us COUNT what we need!

Example: Probability with a Venn Diagram

Class of 40 learners:

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

Filling In the Venn Diagram Step by Step

Step 1: Both sports: 10 learners

Step 2: Calculate "only" regions

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

Step 3: Neither: 40 - (15 + 10 + 8) = 7

Calculating Each Sport's Probability Value

Using our example (40 learners):

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

Find:

• P(only football) = 15/40 = 3/8
• P(only netball) = 8/40 = 1/5

More Probabilities from the Same Diagram

• P(both) = 10/40 = 1/4
• P(neither) = 7/40

Check: 15 + 10 + 8 + 7 = 40, and all probabilities sum to 1

Practice Problem: A Breakfast Survey

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: Filling the Breakfast Diagram

Both = 12

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

Check: 18 + 12 + 13 + 7 = 50 ✓

Solution: The Four Breakfast 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) ✓

Probability Shows Up in Real Life

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

The Key Steps for Any Probability Problem

1. Draw the Venn diagram
2. Fill in numbers, starting with the intersection
3. Calculate the other regions
4. Check the total equals U
5. Calculate probabilities (favorable/total)

Practice: A Quick Pencil 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)

Solving the Pencil Box Problem

Fill Venn diagram:

• Striped: 3, Red only: 15 - 3 = 12, Blue only: 12 - 3 = 9

Probabilities:

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

Summary: Probability and Venn Diagrams

Probability:

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

Venn diagrams: organize information and make counting easier

You've Completed the Sets Topic

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 ✓

Tonight's Homework for Practicing Probability

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

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

3. Write 2-3 sentences on when you'd use probability in daily life.

Preview: Starting Whole Numbers Next

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

Topics include:

• Place value
• Ordering and rounding numbers
• Number operations

Sets knowledge will help you throughout mathematics!

Lesson Credits and Curriculum Source

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!