Question

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

So, there will be $13\times 2=26$ heart or spade cards in a pack.

The favorable outcomes is $26$ and total outcomes is $52$.

Step 2 Finding the probability that the card drawn is a spade or heart 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 $26$ and the total number of outcomes as $52$.

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

Hence, the probability of drawing a card that is a heart or spade card from a pack of $52$ cards is $\frac{1}{2}$.