# A CARD IS DRAWN FROM A PACK OF 52 CARDS AND A GAMBLER BETS THAT IT IS A SPADE OR AN ACE . WHAT ARE THE ODDS AGAINST HIS WINNING THIS BET?PLEASE TELL THAT WHAT IS THE SENSE OF THE LAST STATEMENT OF THIS QUESTION?

the odds against winning is
the number of spade cards = 13
number of ace cards = 4 [including one spade card]
number of spade or ace cards = 13+4-1=16
the probability of getting spade or ace card, i.e. probability of winning = $\frac{16}{52}=\frac{4}{13}$
the probability of losing = $1-\frac{4}{13}=\frac{13-4}{13}=\frac{9}{13}$
therefore odds against winning $=\frac{9/13}{4/13}=\frac{9}{4}$
thus odd against his winning is 9:4

hope this helps you

• 30

It means the propability of his losing or (1-probability of his winning).

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