A card is drawn from a pack of 52 cards and a | vedclass

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(C) The total number of cards is $52$.Let $S$ be the event that the card drawn is a spade,and $A$ be the event that the card drawn is an ace.Number of

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$9$ to $4$

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(C) The total number of cards is $52$.Let $S$ be the event that the card drawn is a spade,and $A$ be the event that the card drawn is an ace.Number of spades $= 13$,so $P(S) = \frac{13}{52}$.Number of aces $= 4$,so $P(A) = \frac{4}{52}$.The card that is both a spade and an ace is the ace of spades,so $P(S \cap A) = \frac{1}{52}$.The probability of winning the bet (drawing a spade or an ace) is $P(S \cup A) = P(S) + P(A) - P(S \cap A) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$.The probability of losing the bet is $1 - P(S \cup A) = 1 - \frac{4}{13} = \frac{9}{13}$.Odds against winning are defined as the ratio of the probability of losing to the probability of winning.Odds against $= \frac{P(	ext{losing})}{P(	ext{winning})} = \frac{9/13}{4/13} = \frac{9}{4}$,which is $9$ to $4$.

$A$ card is drawn from a pack of $52$ cards and a gambler bets that it is a spade or an ace. Which one of the following is the odds against his winning this bet?

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