Question

How do you find the probability of getting a red face card in a deck of $52$ cards?

Answer 1

Find the probability of getting red face card:

There are $52$ cards in a deck of card.

Therefore the total number of possible outcome is $52$.

Total number of face card is $12$

Therefore total number of red face card is $6$

Then the number of possible outcome of event $P\left(A\right)$

$\begin{array}{rcl}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}& \mathbf{=}& \frac{\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{f}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{u}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{p}\mathbf{o}\mathbf{s}\mathbf{s}\mathbf{i}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}\\ & =& \frac{6}{52}\\ & =& \frac{3}{26}\end{array}$

Hence, the probability of getting a red face card is $\frac{\mathbf{3}}{\mathbf{26}}$.