Question

A card is drawn at random from a pack of $52$ playing cards. Find the probability that the card drawn is neither a red card nor a black king.

Answer 1

Step 1: Finding the number of total and favorable outcomes

There are $52$ playing cards.

So, the total number of outcomes are $52$.

In a pack of $52$ playing cards, there are $26$ red cards and $26$ black cards.

There are $4$ suits, $2$ of red and $2$ of black.

Each suit has a king card.

So, $2$ kings are black and $2$ are red.

Now, the number of cards that are neither red nor king are

$52-26-2=24$

So, the number of favorable outcomes are $24$.

Step 2: Finding the probability of getting neither a red card nor a black king

The formula is

$\Rightarrow Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

Let A be the event that the card drawn is neither a red card nor a black king.

$$\begin{gathered} \Rightarrow P\left(A\right)=\frac{24}{52} \\ \therefore P\left(A\right)=\frac{6}{13} \end{gathered}$$

Hence, the probability that the card drawn is neither a red card nor a black king is $\frac{6}{13}$.