Answer
$\dfrac{1}{2}$
Work Step by Step
The sample space has a total of $10$ elements. The numbers greater than $6$ and less than $12$ are $\{7,8,9,10,11\}$. All in all, there are $5$ events that satisfy the condition "greater than $6$ and less than $12$." Hence,
\begin{align*}\require{cancel}
P(\text{greater than $6$ and less than $12$})&=
\dfrac{5}{10}
\\\\&=
\dfrac{\cancel5^1}{\cancel{10}^2}
&\text{(divide by $5$)}
\\\\&=
\dfrac{1}{2}
.\end{align*}
