<p>A card is drawn from a pack of 52 cards. A person bets that it is a spade or an ace. What are the odds against him of winning this bet?</p>
Step-by-Step Solution
Key Concept: Calculate the number of favorable outcomes (spades OR aces) using set theory, accounting for overlap. Odds against = (unfavorable outcomes):(favorable outcomes).
<p><strong>Step 1:</strong> Count favorable outcomes (Spade OR Ace).</p><p>Spades in deck: 13</p><p>Aces in deck: 4</p><p>Ace of Spades: counted in both, so subtract 1 (inclusion-exclusion)</p><p>Favorable outcomes = 13 + 4 - 1 = <strong>16</strong></p><p><strong>Step 2:</strong> Find unfavorable outcomes.</p><p>Unfavorable outcomes = 52 - 16 = <strong>36</strong></p><p><strong>Step 3:</strong> Calculate odds against winning.</p><p>Odds against = (Unfavorable):(Favorable) = <strong>36:16 = 9:4</strong></p><p>∴ Answer: A</p>
Correct Answer: A