Question

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

• A. $\frac{4}{9}$
• B. $\frac{9}{4}$
• C. $\frac{4}{7}$
• D. $\frac{5}{7}$

Answer 1

The correct option is B $\frac{9}{4}$

Probability of winning the bet $=\frac{16}{52}=\frac{4}{13}$
Probability of losing the bet $=1-\frac{16}{52}=\frac{36}{52}=\frac{9}{13}$
Hence odds against his winning
$=\frac{9}{13}:\frac{4}{13}=\frac{9}{4}$