Venn Diagrams
Visualizing sets and calculating probabilities
Sample Space (S)
The rectangle contains all possible outcomes. Total probability within equals 1.
Intersection (A ∩ B)
The overlapping area represents outcomes belonging to both Event A AND Event B.
Union (A ∪ B)
All outcomes in A, B, or both. Used for "OR" probability calculations.
Complement (A')
Everything outside circle A — outcomes NOT in Event A. P(A') = 1 - P(A).
Mutually Exclusive
Circles that don't overlap — no common outcomes (A ∩ B = ∅).
Worked Example: Soccer & Rugby
Problem: In a class of 30 learners, 15 play soccer (A), 10 play rugby (B), and 4 play both sports. Find the probability a random learner plays only soccer.
- Step 1: Fill intersection first: Both = 4
- Step 2: Only Soccer = 15 - 4 = 11
- Step 3: Only Rugby = 10 - 4 = 6
- Step 4: Total playing sports = 11 + 6 + 4 = 21
- Step 5: Neither sport = 30 - 21 = 9
- Step 6: P(Only Soccer) = 11/30
Interactive Venn Diagram Builder
Adjust the numbers to see how the Venn diagram changes. Values update probabilities in real-time!
Probability Calculator
P(B) = 10/30 = 0.333
P(A ∩ B) = 4/30 = 0.133
P(A ∪ B) = 21/30 = 0.700
P(Only A) = 11/30 = 0.367
Set Operation Quiz
Test your knowledge of Venn diagram notation!
Test Your Understanding
Question 1: In a Venn diagram, what does the overlapping region of two circles represent?
Question 2: If P(A) = 0.6 and P(A') is the complement, what is P(A')?
Question 3: Two events that have no outcomes in common are called:
