Question

A card is drawn from a pack of $52$ playing cards. Find the probability that the card drawn is an ace of club or a king of spade.

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.

There is $1$ ace of club and $1$ king of spade card in each pack.

So, there will be $1+1=2$ cards in a pack of favourable outcomes.

The favorable outcomes is $2$ and total outcomes is $52$.

Step 2 Finding the probability that the card drawn is an ace of club or king of spade:

The formula for the 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 $52$.

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

Hence, the probability of drawing a card that is an ace of club or king of spade from a pack of $52$ cards is $\frac{1}{26}$.