Probability of Regular Pack of 52 Cards.

52 card pack

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 (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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