Question

A card is drawn from an ordinary pack 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

The correct option is A 9 : 4

Let A : a spade is drawn and

B : an ace is drawn

Probability of winning the bet = P(A or B)

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

$=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$

Probability of losing the bet

$=1-\frac{4}{13}=\frac{9}{13}$

$Oddsagainstwinningthebet=9:4$