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Union: Cards

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Calculator Dice Coins Marbles Cards Learn

Heart OR Face CardHeart/Face Red OR AceRed/Ace King OR QueenK or Q

Drawing a Red Card OR Ace

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).

Do these events overlap?

Yes! The Ace of Hearts (A♥) and Ace of Diamonds (A♦) are both red AND Aces. We have 2 cards in the overlap.

How to think about it:

We want cards that are red OR Aces — this includes:

All 26 red cards (including the red Aces)
The 2 black Aces (A♣ and A♠)

Total: 26 + 2 = 28 cards. Let's verify with the formula!

Identifying the Events

Question

Draw one card. What's P(Red OR Ace)?

Event A: Red Cards (26 cards)

All 13 Hearts ♥ + All 13 Diamonds ♦

Event B: Aces (4 cards)

One Ace per suit

A♥

A♦

A♣

A♠

The Overlap: Red Aces (2 cards)

These are both red AND Aces — counted twice if we just add!

A♥

A♦

Step-by-Step Calculation

Add the individual probabilities

This double-counts A♥ and A♦

Subtract the overlap (A♥, A♦)

Remove the 2 red Aces counted twice

Result:

Verification by Counting

Think of it this way:

26 red cards (all hearts and diamonds, including red aces)
+ 2 black aces (A♣ and A♠, not counted yet)
= 28 cards total