A single card is drawn uniformly at random from a standard 52-card deck. What is the probability that it is neither a heart nor a king?
Aptitude
Probability
Difficulty: Easy
Choose an option
-
A4/13
-
B9/13
-
C2/13
-
D4/13
-
ENone of these
Answer
Correct Answer: 9/13
Explanation
Introduction / Context:Use inclusion–exclusion to avoid double-counting the king of hearts when excluding hearts and kings from a deck. Then divide by total cards for the probability.
Given Data / Assumptions:
- 52-card standard deck.
- Hearts = 13; Kings = 4; overlap (king of hearts) = 1.
Concept / Approach:
- Cards that are heart or king = 13 + 4 − 1 = 16 (by inclusion–exclusion).
- “Neither” count = 52 − 16 = 36.
- Probability = 36/52 = 9/13.
Step-by-Step Solution:
Count(forbidden) = 13 + 4 − 1 = 16Count(allowed) = 52 − 16 = 36Probability = 36/52 = 9/13Verification / Alternative check:Complement method directly: P(neither) = 1 − P(heart ∪ king) = 1 − 16/52 = 36/52 = 9/13.
Why Other Options Are Wrong:
- 4/13 and 2/13 correspond to the complement or partial counts.
- Duplicate 4/13 remains incorrect; “None of these” is false because 9/13 is correct.
Common Pitfalls:
- Double-counting the king of hearts if adding 13 and 4 without subtracting 1.
Final Answer:9/13