Answer
The probability that a 5 or a black card is dealt from a pack of 52 cards is $\frac{7}{13}$.
Work Step by Step
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 $\frac{7}{13}$.
