Union and Intersection

Understanding "And" (∩) and "Or" (∪) in Probability

CAPS Grade 10 | Mathematics

Intersection (A ∩ B)

The OVERLAPPING area — outcomes in BOTH sets. Keyword: "AND"

Union (A ∪ B)

The ENTIRE shaded area — outcomes in A OR B OR both. Keyword: "OR"

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!

Set A: { }

Set B: { }

Intersection (A ∩ B): { }

Union (A ∪ B): { }

P(A): 0/10 = 0

P(B): 0/10 = 0

P(A ∩ B): 0/10 = 0

P(A ∪ B): 0/10 = 0

Addition Rule Check: 0 + 0 - 0 = 0

Quick Quiz

Q1: What does the symbol ∩ represent?

Union (Or)

Intersection (And)

Complement

Q2: If P(A)=0.6, P(B)=0.3, P(A∩B)=0.1, what is P(A∪B)?

0.8

0.9

0.7

1.0

Q3: Why do we subtract P(A∩B) in the Addition Rule?

Because it's counted twice

Because it's impossible

To add it again

Key Takeaways

∩ (Intersection): "AND" — outcomes in both sets

∪ (Union): "OR" — outcomes in A, B, or both

Addition Rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Mutually Exclusive: If no overlap, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B)

Key Terms

Intersection Union Addition Rule Mutually Exclusive Overlap Sample Space

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