Question

Melanie has drawn a card from a well-shuffled deck of $52$ cards. What is the probability of drawing a card either being red or a king?

• A. $\frac{15}{26}$
• B. $\frac{7}{13}$
• C. $\frac{1}{2}$
• D. $\frac{1}{13}$

Answer 1

The correct option is B $\frac{7}{13}$

Suppose, $\text{E}$ is an event of drawing a card either being red or a king from a well-suffled deck of $52$ cards.

$\therefore$ Total number of possible outcomes= $52$

There are $26$ red cards ($13$ diamonds + $13$ hearts), and $\text{4 (2 red+2 black)}$ kings in the deck. If we add $26$ and $4$ to find the number of cards either being red or king, we will be counting $\text{2 red}$ cards twice because out of $4$ kings, $2$ red kings are already included in $26$ red cards.

Thus, the correct number of outcomes which are favorable to the event $\text{E}$ is $26+4-2=28$.

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

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

$\Rightarrow \text{P(E)}=\frac{28}{52}=\frac{4\times 7}{4\times 13}=\frac{7}{13}$


$\therefore$ The probability of drawing a card either being red or a King is $\frac{7}{13}$.