Question

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

So, there will be $4$ cards of queen in a pack.

The favorable outcomes is $4$ and total outcomes is $52$.

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

The formula for the probability is expressed as,

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

Substitute favorable number outcomes as $4$ and total number of outcomes as $52$.

$$\begin{gathered} \Rightarrow P\left(cardisaqueen\right)=\frac{4}{52} \\ \therefore P\left(cardisaqueen\right)=\frac{1}{13} \end{gathered}$$

Hence, the probability of drawing a card that is a queen from a pack of $52$ cards is $\frac{1}{13}$.