Set Theory Basics 📚
Probability uses the language of Sets.
- Sample Space (S) = Universal Set
- Event (E) = Subset
Operations on Events ⚙️
1. Union of Sets (A ∪ B) 🟠
Represents "A or B" (or both).
- All elements that are in A, or in B, or in both.
- Probability:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
2. Intersection of Sets (A ∩ B) 🔴
Represents "A and B".
- Common elements shared by both sets.
- If
A ∩ B = φ(Empty), they are Mutually Exclusive.
3. Complement of a Set (A' or Ā) ⚪
Represents "Not A".
- All outcomes in Sample Space that are NOT in A.
P(A') = 1 - P(A)
Visual Summary 🖼️
➕
OR
Union ∪
✖️
AND
Intersection ∩
⛔
NOT
Complement A'
🚫
Impossible
Empty Set φ
The "At Least One" Rule 💡
Often we are asked to find probability of "At Least One" success. It is easier to calculate "None" and subtract from 1.
P(At least one) = 1 - P(None)
Test Your Knowledge
Question 1 of 3
1. A ∪ B represents: