Multiple choice

A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are

  1. 9 : 4

  2. 35 : 17

  3. 17 : 35

  4. 4 : 9
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A Correct answer
Explanation

Total cards = 52. Spade = 13. Ace = 4. One ace is a spade, so total favorable outcomes = 13 + 3 = 16. Probability of winning = 16/52 = 4/13. Probability of losing = 1 - 4/13 = 9/13. Odds against winning = (9/13) / (4/13) = 9:4.

AI explanation

There are 13 spades and 3 other aces in a deck of 52 cards, so there are 16 favorable outcomes for winning. The number of unfavorable outcomes is 52 - 16 = 36. The odds against winning are the ratio of unfavorable outcomes to favorable outcomes, which is 36/16 or 9:4.

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