Question

In a deck of cards, find the probability of getting a spade.

Answer 1

Find the probability of getting a spade:

In a deck of cards, there are $13$ Hearts, $13$ Diamonds, $13$ Spades, and $13$ Clubs.

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

The number of spades, $n\left(S\right)=13$.

We know that the probability of an event $=\frac{\mathrm{Number}\mathrm{of}\mathrm{ways}\mathrm{that}\mathrm{event}\mathrm{can}\mathrm{occur}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcome}}$

Thus, the probability of getting a spade, $\mathit{P}\left(S\right)\mathbf{=}\frac{\mathbf{n}\left(S\right)}{\mathbf{n}\left(T\right)}$.

$$\begin{gathered} \Rightarrow P\left(S\right)=\frac{13}{52} \\ \Rightarrow P\left(S\right)=\frac{1}{4} \end{gathered}$$

Therefore, the probability of getting a spade is $\frac{1}{4}$.