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Intersection: Cards

P(A ∩ B) - cards satisfying BOTH conditions

Drawing the King of Hearts

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 be both:

This is a very specific request — only ONE card in the entire deck fits!

Why is the intersection so small?

Each suit has exactly ONE King. Since we're specifying both the suit (Hearts) and the rank (King), we've pinpointed a single card out of 52.

This is like asking for a specific cell in a grid

A deck is like a 4×13 grid (4 suits × 13 ranks). Specifying "Heart AND King" is like asking for row = Hearts, column = King — exactly one cell.

All 13 hearts: A♥ through K♥

K♥

K♦

K♣

K♠

K♥

Only the K♥ is both a Heart AND a King

List all Hearts

A♥, 2♥, 3♥, 4♥, 5♥, 6♥, 7♥, 8♥, 9♥, 10♥, J♥, Q♥, K♥ = 13 cards

List all Kings

K♥, K♦, K♣, K♠ = 4 cards

Find the intersection (cards in BOTH lists)

Only K♥ appears in both lists = 1 card

Result:

For ANY combination of one specific suit and one specific rank:

Examples: P(Ace of Spades) = 1/52, P(7 of Diamonds) = 1/52, P(Queen of Clubs) = 1/52

This is because 4 suits × 13 ranks = 52 unique combinations, and each combination is exactly one card.