Question

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

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 is labeled as spades, clubs, diamonds and hearts.

The suits are divided into two colors of red: diamonds and hearts and black: spades and clubs

There are $3$ face cards in each suit labeled as king, queen and jack.

So, there will be $3\times 2=6$ black face cards in a pack.

The favorable outcomes is $6$ and total outcomes is $52$.

Step 2 Finding the probability that the card drawn is a black face card:

The formula for the probability is expressed as,

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

Substitute favorable number of outcomes as $6$ and the total number of outcomes as $52$.

$$\begin{gathered} \Rightarrow P\left(cardisablackfacecard\right)=\frac{6}{52} \\ \therefore P\left(cardisablackfacecard\right)=\frac{3}{26} \end{gathered}$$

Hence, the probability of drawing a card that is a black face card from a pack of $52$ cards is $\frac{3}{26}$.