Mutually Exclusive Events 🙅‍♂️

Two or more events are said to be Mutually Exclusive (or Disjoint) if they cannot occur at the same time.

[!NOTE] Rule: If Event A happens, Event B simply cannot happen. A ∩ B = φ (Intersection is empty). P(A and B) = 0.

Examples 📝

1. Coin Toss: You can get Head OR Tail. You cannot get both.
   • H and T are Mutually Exclusive.
2. Card Game: Drawing a King OR a Queen.
   • A card cannot be both a King and a Queen.
3. Exam Result: Pass OR Fail.

Non-Mutually Exclusive (Compatible) Events 🤝

Events that can happen together.

• Example: Drawing a "King" and a "Heart" from a deck.
  • Can you draw a card that is both? Yes! The "King of Hearts".
  • So, "King" and "Heart" are NOT mutually exclusive.

Visualization 🖼️

• Mutually Exclusive: Two separate circles that do NOT touch.
• Not Mutually Exclusive: Two overlapping circles (Venn Diagram).

Why is this important? 🌟

It determines which formula to use for the Addition Theorem:

• If Mutually Exclusive: P(A or B) = P(A) + P(B)
• If NOT: P(A or B) = P(A) + P(B) - P(A and B)

Loading quiz…