Probability
Classical Probability
Grade 12

Question:

<p>A card is drawn at random from a pack of cards. What is the probability that the drawn card is neither a heart nor a king?</p>
<p>\(\dfrac{9}{52}\)</p>
<p>\(\dfrac{9}{13}\)</p>
<p>\(\dfrac{4}{13}\)</p>
<p>\(\dfrac{3}{13}\)</p>

Step-by-Step Solution

Key Concept: Use complementary counting: find cards that are hearts OR kings, then subtract from total. Remember the king of hearts is counted only once.
<p><strong>Step 1:</strong> Find cards that are hearts OR kings using inclusion-exclusion principle.</p><p>• Hearts in deck = 13</p><p>• Kings in deck = 4</p><p>• King of hearts (counted in both) = 1</p><p><strong>Step 2:</strong> Cards that are hearts OR kings = 13 + 4 - 1 = 16</p><p><strong>Step 3:</strong> Cards that are neither hearts nor kings = 52 - 16 = 36</p><p><strong>Step 4:</strong> Probability = 36/52 = 9/13</p><p>∴ Answer: B</p>
Correct Answer: B

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