Question

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

• A. $9:4$
• B. $4:9$
• C. $5:9$
• D. $9:5$

Answer 1

Answer: (A)

Let events A: a spade is drawn and event B: an ace is drawn.

The probability of winning the bet$=P\left(AorB\right)$

$P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}$ (There is one ace of spades)

$=\frac{16}{52}=\frac{4}{13}$

$\therefore$ Probability of losing the bet$=1-\frac{4}{13}=\frac{9}{13}$

$\therefore$ Odds against winning the bet$=\frac{9}{13}:\frac{4}{13}=9:4$.