Question

What is the probability of drawing a red card from a well-suffled pack of $52$ cards?

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{1}{2}$

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

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

And, as there are two red suits (diamonds, hearts) with $13$ cards each, the total number of red cards= $2\times 13=26$.

$\therefore$ Number of favorable outcomes of the event $\text{E}$= number of red cards in the pack of $52$ cards= $26$

Hence,

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

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

$\Rightarrow \text{P (E)}=\frac{26}{52}=\frac{26}{2\times 26}=\frac{1}{2}$

$\therefore$ The probability of drawing a red card from a well-suffled pack of $52$ cards is $\frac{1}{2}$.