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