Question

A card is drawn from a well-shuffled deck of $52$ cards.

Find the probability of getting a king of the red suits.

Answer 1

Find the probability of getting a king of the red suits:

Probability of an event $E$ is defined by $P\left(E\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$

The total number of cards, $n\left(T\right)=52$.

There are two kings of the red suits, it is either the king of hearts or the king of diamonds.

Thus, the number of kings of the red suits, $n\left(K\cap R\right)=2$.

Therefore, the probability of getting a king of the red suits can be given by, $P\left(K\cap R\right)=\frac{n\left(K\cap R\right)}{n\left(T\right)}$.

$$\begin{gathered} \Rightarrow P\left(K\cap R\right)=\frac{2}{52} \\ \Rightarrow P\left(K\cap R\right)=\frac{1}{26} \end{gathered}$$

Hence, the probability of getting a king of the red suits is $\frac{1}{26}$.