# Probability of Regular Pack of 52 Cards.

## Example

A card is selected from a regular pack of $52$ cards. Find the probability that it is neither black nor a picture card.

There are $26$ black cards, $6$ black picture cards $\text{(J, Q, K)}$ and $6$ red picture cards. 6 black picture cards are included in 26 black cards. So the number of cards that are neither black nor picture cards is all cards – black cards – red picture cards.

\begin{align} \Pr(\text{neither black or a picture card}) &= 1-\Pr(\text{black})-\Pr(\text{red picture}) \\ &= \displaystyle 1-\frac{26}{52}-\frac{6}{52} \\ &= \frac{20}{52} \\ &= \frac{5}{13} \end{align}