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A standard deck has 52 cards: 4 suits × 13 ranks. Red = Hearts + Diamonds (26 cards). Face cards = J, Q, K (12 cards).
What exactly are we looking for?
A card must satisfy both conditions simultaneously:
What is a face card?
Face cards are the "picture" cards: Jack (J), Queen (Q), and King (K). There are 3 face cards per suit × 4 suits = 12 face cards total. Note: Aces are NOT face cards.
Strategy: Find the overlap
Instead of multiplying probabilities (which works for independent events), we need to count cards that are in both categories. Card properties like color and rank are NOT independent — they're fixed together on each card!
All Hearts ♥ and Diamonds ♦
All Jacks, Queens, Kings
J♥, Q♥, K♥, J♦, Q♦, K♦
Identify all red face cards by systematically checking
Hearts face cards: J♥, Q♥, K♥ = 3 cards
Diamonds face cards: J♦, Q♦, K♦ = 3 cards
Count the total favorable outcomes
3 + 3 = 6 cards that are both red AND face cards
Apply the basic probability formula
Result:
You might wonder: can we use P(Red) × P(Face) = ½ × 12/52?
No! The multiplication rule only works for independent events. When drawing a single card, "red" and "face" are properties of the same card — they're not separate events.
For intersections on a single draw, always count the cards that satisfy both conditions directly.