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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 🖼️

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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)

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