A single card can't be both a heart AND a club. Roll a die — you can't get a 2 AND a 5. Events that can't co-occur have a beautifully simple rule: just add.
Two events are mutually exclusive (disjoint) if they can't both happen. For them, P(A or B) = P(A) + P(B).
Categorising outcomes, computing 'at least one of these' probabilities, partitioning a sample space — knowing when you can just add is essential.
Drawing one card: are 'it's a King' and 'it's a Queen' mutually exclusive?
If A and B can overlap, you've double-counted the overlap — subtract P(A and B) once to fix it.
Roll a die. P(a 1 OR a 6)?
Draw a card. P(it's a King OR a Heart)?
NOT exclusive (King of Hearts overlaps). P(King) = 4/52, P(Heart) = 13/52, P(both) = 1/52. So 4/52 + 13/52 − 1/52 = 16/52 = 4/13.
Don't just add when events can overlap. P(King) + P(Heart) = 17/52 double-counts the King of Hearts. Always check: can both happen at once?
Mutually exclusive ≠ independent. Exclusive events are *strongly dependent* — if one happens, the other definitely doesn't. They're almost opposite ideas.
- Mutually exclusive = can't both happen.
- Then P(A or B) = P(A) + P(B).
- If they can overlap, subtract P(A and B) to avoid double-counting.