Question

The probability of drawing a face card from a pack of well-shuffled deck of $52$ cards is .

• A. $\frac{3}{13}$
• B. $\frac{4}{13}$
• C. $\frac{5}{13}$

Answer 1

The correct option is A $\frac{3}{13}$

In a deck of $52$ cards, for each of four suits, we have $3$ face cards (Jack, King and Queen). Hence, including all four suits, we have $3\times 4=12$ face cards out of $52$ cards.

Therefore,
$\bullet$ Total number of possible outcomes= Total number of cards in the deck= $52$
$\bullet$ Number of favorable outcomes= Number of face cards= $12$

Now,

$\text{P (drawing a face card)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
$\Rightarrow \text{P (drawing a face card)}=\frac{12}{52}=\frac{4\times 3}{4\times 13}=\frac{3}{13}$

$\therefore$ The probability of drawing a face card from a well-shuffled pack of $52$ cards is $\frac{3}{13}$.