Question

Question: What is the probability that a card selected at random from a standard deck of $\mathbf{52}$cards is an ace?

Short answer

Answer

The probability that a card selected at random from a standard deck of $52$cards is an ace is$P\left(E\right)=\frac{1}{13}$

Step-by-step solution

Given  

As per the problem a card is selected at random from a standard deck of 52 cards.

Explanation of Solution  

Ifrepresents the sample spaceandrepresents the event. Then the probability of occurrence of favourable event is given by the formula as below:

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Here we have a standard deck of cards so we have$n\left(S\right)=52$

As there are four aces in a standard deck of cards so we have$n\left(E\right)=4$

Now substitute the values in the above formula we get

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