Question

Kyra is playing with cards. If a card is drawn from a pack of 52 cards, what is the probability of not getting a face card nor an ace?

• A. $\frac{9}{13}$
• B. $\frac{8}{13}$
• C. $\frac{1}{13}$
• D. $\frac{4}{13}$

Answer 1

The correct option is A $\frac{9}{13}$

$\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Number of face cards = 12 (4 Jacks, 4 Queens, and 4 Kings)

$\text{Probability of getting a face card}$
$=\frac{\text{Number of face cards}}{\text{Total number of outcomes}}$

$=\frac{12}{52}$

$\text{Number of ace cards = 4}$

$\text{Probability of getting an ace card}$
$=\frac{\text{Number of ace cards}}{\text{Total number of outcomes}}$

$=\frac{4}{52}$

$\text{Probability of getting a face or an ace card}$

$=\text{Probability of getting (face + ace) cards}$

$=\frac{12}{52}+\frac{4}{52}$

$=\frac{16}{52}⟹\frac{4}{13}$

$\text{Probability of not getting face or ace cards}$
$=1–\text{Probability of getting (face + ace) cards}$

$=1–\frac{4}{13}$

$=\frac{13–4}{13}$

$=\frac{9}{13}$