Question

A card is chosen at random from a well-suffled deck of $52$ playing cards. The probability of choosing a card that is not a queen is .

• A. $\frac{1}{13}$
• B. $\frac{12}{13}$
• C. $\frac{13}{12}$
• D. $\frac{13}{52}$

Answer 1

The correct option is B $\frac{12}{13}$

For choosing a queen card from a well-suffled deck of $52$ playing cards,

$\bullet$ total number of outcomes= number of cards in the deck= $52$
$\bullet$ number of favorable outcomes= number of queen cards in the deck= $4$

$\therefore \text{P(choosing queen)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

$\Rightarrow \text{P(choosing queen)}=\frac{\text{Number of queens in the deck}}{\text{Total number of cards in the deck}}$

$\Rightarrow \text{P(choosing queen)}=\frac{4}{52}=\frac{4\times 1}{4\times 13}=\frac{1}{13}$

We know,
$\text{P(not choosing queen)}=1-\text{P(choosing queen)}$

$\Rightarrow \text{P(not choosing queen)}=1-\frac{1}{13}$

$\Rightarrow \text{P(not choosing queen)}=\frac{13}{13}-\frac{1}{13}=\frac{13-1}{13}=\frac{12}{13}$

$\therefore$ The probability of NOT choosing queen from a well-suffled deck of $52$ cards is $\frac{12}{13}$.