Question

David draws a card from a well-suffled pack of $52$ cards. What is the probability that David draws a red numbered card?

• A. $\frac{5}{26}$
• B. $\frac{7}{26}$
• C. $\frac{9}{26}$
• D. $\frac{11}{26}$

Answer 1

The correct option is C $\frac{9}{26}$

Let $\text{E}$ is an event of drawing a red numbered card from a well-suffled pack of $52$ cards.

As there are $52$ cards in the deck, total number of possible outcomes= number of cards in the deck= $52$.

There are $9$ numbered cards ($2$ to $10$) in each of the four suits, and there are $2$ red suits (diamonds and hearts).

$\therefore$ Number of favorable outcomes for drawing a red numbered card= Total number of red numbered cards in the deck= $9\times 2=18$

Hence,
$\text{P (E)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P (E)}=\frac{\text{Number of red numbered cards}}{\text{Total number of cards}}$

$\Rightarrow \text{P(E)}=\frac{18}{52}=\frac{2\times 9}{2\times 26}=\frac{9}{26}$

$\therefore$ The probability of drawing a red numbered card from a well-suffled pack of $52$ cards is $\frac{9}{26}$.