Question

Shane correctly determines the probability of drawing a red queen from a well-shuffled pack of $52$ cards as .

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

Answer 1

The correct option is B $\frac{1}{26}$

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

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

There are total $4$ queens in pack, out of which $2$ are red. Therefore, for drawing a red queen, number of favorable outcomes= number of red queens= $2$.

Now,

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

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

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

$\therefore$ The probability of drawing a red queen from a well-suffled pack of $52$ cards is $\frac{1}{26}$.