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A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is a King or a Heart?

4/13

16/52

17/52

1/4

Correct Answer

⚙️ TE • Technical Addition PrincipleMathematicsStatistics and Probability

Option A

4/13

Quick Summary:

Count total favorable outcomes: 4 Kings + 13 Hearts - 1 (the King of Hearts counted twice) = 16. Divide by 52 to get 16/52 = 4/13.

📐MAMath SolutionAddition Principle

📋 Given

A deck has 52 cards. We need to find the probability of drawing a King (K) or a Heart (H).

🔢 Formula Used

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)P(A∪B)=P(A)+P(B)−P(A∩B)

⚡ Exam Hall Shortcut / Speed Trick

Count total favorable outcomes: 4 Kings + 13 Hearts - 1 (the King of Hearts counted twice) = 16. Divide by 52 to get 16/52 = 4/13.

⚠️ Common Student Trap / Pitfall

Students often add 4 Kings and 13 Hearts to get 17 outcomes, forgetting that the King of Hearts is a member of both groups and is being counted twice.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify individual probabilities

There are 4 Kings in a deck and 13 Hearts. The probability of picking a King is $P(K) = 4/52$ and a Heart is $P(H) = 13/52$ .

P(K)=452,P(H)=1352P(K) = \frac{4}{52}, \quad P(H) = \frac{13}{52}P(K)=524​,P(H)=5213​

Identify the intersection

There is exactly 1 card that is both a King and a Heart (the King of Hearts).

P(K∩H)=152P(K \cap H) = \frac{1}{52}P(K∩H)=521​

Apply Addition Theorem

Combine the probabilities while subtracting the overlap to avoid double counting.

P(K∪H)=452+1352−152P(K \cup H) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52}P(K∪H)=524​+5213​−521​

Final Calculation

Sum the numerators: $4 + 13 - 1 = 16$ . Divide by the denominator 52 and simplify the fraction.

1652=413\frac{16}{52} = \frac{4}{13}5216​=134​

✅

A is correct because the application of the inclusion-exclusion principle results in $16/52$ , which simplifies to $4/13$ .

Core Concepts Used

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Probability of Union Inclusion-Exclusion Principle Deck of Cards Composition

💡 EXAM TIP

This principle of $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ is the foundation for solving Set Theory problems in Data Interpretation.

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