A∩B
A and B both occur.
🎯 Learning Objectives
- read probability information from Venn diagrams;
- calculate unions, intersections and complements;
- convert frequencies into probabilities;
- connect set notation to probability language.
Introduction
This lesson develops Venn-Diagram Probability from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Set and Probability Language
A∪B
A or B or both occur.
A′
A does not occur.
Outside both
Neither A nor B occurs.
Worked Example
In a group of 40 learners: 18 study French, 15 study Shona and 6 study both.
French only=18−6=12.
Shona only=15−6=9.
Union=12+6+9=27.
P(F∪S)=27/40.
Neither=40−27=13, so P(neither)=13/40.
Practice Questions
- Using the example, find P(F∩S).
- Find P(F only).
- Find P(not F).
- Verify the union using 18+15−6.
✅ Check Your Work
Show answers and working
- 6/40=3/20.
- 12/40=3/10.
- Not F includes Shona-only and neither: (9+13)/40=22/40=11/20.
- 18+15−6=27, matching the region total.
🧪 Math Lab: Venn Regions
Click a region name to highlight the meaning.
Choose a region.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.