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