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A standard deck has 52 cards: 4 suits (Hearts ♥, Diamonds ♦, Clubs ♣, Spades ♠) × 13 ranks. Face cards are Jack, Queen, King (12 total). Red cards are Hearts + Diamonds (26 total).
Can a card be BOTH a King AND a Queen?
No! Every card has exactly one rank. A card is either a King, or a Queen, or something else entirely. There's no overlap between these events.
What does "mutually exclusive" mean again?
Events are mutually exclusive when they cannot happen at the same time. If you draw a King, you definitely did NOT draw a Queen (and vice versa).
The Simplification:
Since P(King AND Queen) = 0, the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B) becomes just P(A) + P(B). No subtraction needed!
Draw one card. What's P(King OR Queen)?
One King per suit
One Queen per suit
Impossible! No card has two ranks. A card cannot be both a King and a Queen.
Check: Are these mutually exclusive?
Yes! A card cannot be both King and Queen. P(K ∩ Q) = 0.
Use the simplified formula (just add)
Since there's no overlap, no subtraction is needed.
Simplify the fraction
Result:
✓ Verification: 8 cards (4 Kings + 4 Queens) out of 52 = 8/52 ✓
| Event A OR B | Count | Probability |
|---|---|---|
| King OR Queen | 8 | |
| Ace OR King | 8 | |
| Any Face Card (J, Q, or K) | 12 | |
| Heart OR Spade (suit) | 26 |