Question

A card is drawn from a pack of $52$ playing cards. Find the probability that the card drawn is a red queen.

Answer 1

Step 1 Finding the favorable outcomes:

There are $52$ cards in a pack, each pack contains $4$ suits of $13$ cards each.

Each suit which is labeled as spades, clubs, diamonds and hearts contains of $1$ queen card each.

There are $2$ colors in the pack of cards, black for spades and clubs, and red for hearts and diamonds.

So, there will be $1$ queen card in a pack and there are $2$ red packs.

The favorable outcomes is $1\times 2=2$ and total outcomes is $52$.

Step 2 Finding the probability that the card drawn is a red queen:

The formula for probability is expressed as,

$Probability=\frac{Number of favorable outcomes}{Total number of outcomes}$

Substitute favorable number of outcomes as $2$ and the total number of outcomes as $52$.

$$\begin{gathered} \Rightarrow P\left(cardisaredqueen\right)=\frac{2}{52} \\ \therefore P\left(cardisaredqueen\right)=\frac{1}{26} \end{gathered}$$

Hence, the probability of drawing a card that is a red queen from a pack of $52$ cards is $\frac{1}{26}$.