## Precalculus (6th Edition) Blitzer

The probability that a 5 or a black card is dealt from a pack of 52 cards is $\frac{7}{13}$.
We know that the total number of "5" cards in a deck is 4. \begin{align} & P\left( 5 \right)=\frac{\text{number of 5 cards}}{\text{total number of cards in the deck}} \\ & =\frac{4}{52} \\ & =\frac{1}{13} \end{align} And the total number of black cards in a deck is 26. \begin{align} & P\left( \text{black} \right)=\frac{\text{number of black cards}}{\text{total number of cards in the deck}} \\ & =\frac{26}{52} \\ & =\frac{1}{2} \end{align} And the total number of black 5 cards in a deck is 2. \begin{align} & P\left( \text{5 or black} \right)=\frac{\text{number of black 5 cards}}{\text{total number of cards in the deck}} \\ & =\frac{2}{52} \\ & =\frac{1}{26} \end{align} Therefore, the probability that a 5 or a black card is dealt is given below, \begin{align} & P\left( \text{a 5 or a black card} \right)=P\left( 5 \right)+P\left( \text{black} \right)-P\left( \text{5 or black} \right) \\ & =\frac{1}{13}+\frac{1}{2}-\frac{1}{26} \\ & =\frac{7}{13} \end{align} Hence, the probability that a 5 or a black card is dealt is $\frac{7}{13}$.