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Intersection: Cards

P(A ∩ B) - cards satisfying BOTH conditions

Drawing a Black Even-Numbered Card

A standard deck has 52 cards: 4 suits × 13 ranks. Red = Hearts + Diamonds (26 cards). Face cards = J, Q, K (12 cards).

Breaking down the question:

We need a card that satisfies both conditions:

What counts as an "even-numbered" card?

Only the numbered cards 2, 4, 6, 8, 10 are even. That's 5 cards per suit. Face cards (J, Q, K) and Aces don't count — they're not numbers!

Our strategy

Count even-numbered cards in Clubs + even-numbered cards in Spades. Each black suit contributes 5 even cards (2, 4, 6, 8, 10).

♣♠

2, 4, 6, 8, 10 in each suit

2♣

4♣

6♣

8♣

10♣

2♠

4♠

6♠

8♠

10♠

5 even cards in Clubs + 5 even cards in Spades = 10

Count even cards in Clubs ♣

2♣, 4♣, 6♣, 8♣, 10♣ = 5 cards

Count even cards in Spades ♠

2♠, 4♠, 6♠, 8♠, 10♠ = 5 cards

Add them up (no overlap — different suits)

5 + 5 = 10 black even cards total

Result:

Let's verify the count another way:

Event A	Event B	\|A ∩ B\|
Red	Face	6
Black	Even	10
Heart	King	1
Face	Ace	0