Union and Intersection
Understanding "And" (∩) and "Or" (∪) in Probability
Worked Example: Numbers 1 to 10
Event A (Even numbers): {2, 4, 6, 8, 10}
Event B (Multiples of 5): {5, 10}
Intersection (A ∩ B): {10} → P = 1/10 = 0.1
Union (A ∪ B): {2, 4, 5, 6, 8, 10} → P = 6/10 = 0.6
Check: 0.5 + 0.2 - 0.1 = 0.6 ✓
Interactive: Build Your Own Sets
Click on numbers to add them to Set A (Blue) or Set B (Pink). Click again to cycle through options!
Quick Quiz
Q1: What does the symbol ∩ represent
Q2: If P(A)=0.6, P(B)=0.3, P(A∩B)=0.1, what is P(A∪B)
Q3: Why do we subtract P(A∩B) in the Addition Rule
Key Takeaways
Key Terms
How to Read Union and Intersection Questions
Focus on the wording. Union means everything in set A or set B or both, while intersection means only the overlap that belongs to both sets. In Venn diagrams, shading the correct region before calculating can prevent many counting errors.
When using the formula for two sets, remember that the overlap is counted twice if you simply add the totals. Subtract the intersection once so that each item is counted only once. This is the main idea behind most union and intersection calculations.
For word problems, translate phrases carefully. "A or B" usually points to union, "A and B" points to intersection, and "only A" means the part of A outside the overlap. Writing these phrases next to the diagram helps you choose the correct region.
Check your final answer against the diagram. A union cannot be smaller than the intersection, and an "only" region cannot include the overlap. These quick reasonableness checks catch many mistakes before marking.
If a question gives totals for two groups, write the intersection in the overlap first. Then subtract from each group total before filling the outside parts of the circles.
Finally, add all regions to confirm the total sample space before writing the final probability.
