Answer
The required probability is, $\frac{3}{13}$
Work Step by Step
Note that with 52 cards in the deck, the total number of possible ways in which a single card is dealt is 52.
We know that the total number of possible outcomes in the sample space is 52. That is, $ n\left( S \right)=52$
Assume $ E $ to be the event of being dealt a card greater than 3 and less than 7; therefore, $ E=4\text{ or 5 or 6}$ and each of these number can occurs in 12 different ways; therefore, $ n\left( E \right)=12$
Thus, the probability of being dealt a card greater than 3 and less than 7 is:
$\begin{align}
& P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\
& =\frac{12}{52} \\
& =\frac{3}{13}
\end{align}$
