Question

A card is drawn from the deck of playing cards and a gambler bets that it is either a spade or an ace. What are the odds against his winning this bet?

• A.
  $\frac{1}{13}$
• B.
  $\frac{9}{4}$
• C.
  $\frac{2}{13}$
• D.
  $\frac{5}{13}$

Answer 1

The correct option is B

$\frac{9}{4}$
Total number of cards = 52
Total number of spade cards = 13
Total number of ace cards = 4
Let the event for picking a card that is either spade or ace be E.

Out of 13 spade cards, 1 is an ace card.

$\therefore$ Number of outcomes favourable to $E=13+4–1=16$

Also, number of outcomes unfavourable to $E=52–16=36$

Now, odds against an event is given by number of unfavourable outcomes to the number of favourable outcomes.

$\therefore \text{Odds against winning the bet}=\frac{36}{16}=\frac{9}{4}$


Hence, the correct answer is option b.