3-Set Venn Diagrams

3-Set Probability Problems

Venn Diagram

Demographics Study

Events:

A: Woman (P = 0.5)

B: Unemployed (P = 0.2)

C: Academic (P = 0.62)

Given Constraints:

P(A ∩ Bᶜ) = 0.4

P(A ∩ Cᶜ) = 0.18

8 Possible Outcomes:

#1: A∩B∩C= Woman AND Unemployed AND Academic

0.080

#2: A∩B∩Cᶜ= Woman AND Unemployed AND NOT Academic

0.020

#3: A∩Bᶜ∩C= Woman AND NOT Unemployed AND Academic

0.240

#4: A∩Bᶜ∩Cᶜ= Woman AND NOT Unemployed AND NOT Academic

0.160

#5: Aᶜ∩B∩C= NOT Woman AND Unemployed AND Academic

0.300

#6: Aᶜ∩B∩Cᶜ= NOT Woman AND Unemployed AND NOT Academic

0.100

#7: Aᶜ∩Bᶜ∩C= NOT Woman AND NOT Unemployed AND Academic

0.000

#8: Aᶜ∩Bᶜ∩Cᶜ= NOT Woman AND NOT Unemployed AND NOT Academic

0.100

• Click segments to select/deselect

• Hover to preview outcomes

• All 8 segments sum to 1.0

Basic Three-Set Operations

Key Probability Concepts

Interactive Examples

Understanding 3-Set Venn Diagrams

Three-set Venn diagrams show relationships between three events A, B, and C. They reveal complex interactions including triple intersections and various combinations of unions and complements.

Basic Three-Set Operations

Three-set Venn diagrams contain eight distinct regions representing all possible combinations of the three sets and their complements.

Learn More

Key Probability Concepts

Use 3-set diagrams for complex probability calculations including the inclusion-exclusion principle for three events.

Learn More

Interactive Examples

Adjust the diagram regions to see how probabilities change. Each region represents a unique outcome in the sample space.

Learn More