Answer
The probability of getting a number greater than 4 and less than 3 is $\frac{2}{3}$.
Work Step by Step
We know that there are six outcomes in a dice i.e.$\left( \text{S} \right)\text{ = }\left\{ 1,2,3,4,5,6 \right\}$, so $\text{n}\left( \text{S} \right)=\text{ 6}$.
And the event of getting a number less than $3$ can be represented by
${{\left( \text{E} \right)}_{\text{less than 3}}}\text{ }=\text{ }\left\{ 1,2 \right\}$
Since there are two outcomes in this event, $\text{n}{{\left( \text{E} \right)}_{\text{less than 3}}}=\text{ 2}$.
And the probability of getting a number less than $3$ is
$\text{P}{{\left( \text{E} \right)}_{\text{less than 3}}}\text{ = }\frac{\text{n}{{\left( \text{E} \right)}_{\text{less than 3}}}}{\text{n}\left( \text{S} \right)}\text{ = }\frac{2}{6}\text{ }$.
And the event of getting a number greater than $4$ can be represented by
${{\left( \text{E} \right)}_{\text{greater than 4}}}\text{ }=\text{ }\left\{ 5,6 \right\}$
There are two outcomes in this event, so $\text{n}{{\left( \text{E} \right)}_{\text{greater than 4}}}=\text{ 2}$.
And the probability of getting a number greater than 4 is given below,
$\text{P}{{\left( \text{E} \right)}_{\text{greater than 4}}}\text{ = }\frac{\text{n}{{\left( \text{E} \right)}_{\text{greater than 4}}}}{\text{n}\left( \text{S} \right)}\text{ = }\frac{2}{6}\text{ }$.
Therefore, the probability of getting a number less than 3 or greater than 5 is
$\begin{align}
& {{\text{P}}_{\text{less than 3 or greater than 4}}}\text{ = }{{\text{P}}_{\text{less than 3}}}+\text{ }{{\text{P}}_{\text{greater than 4}}} \\
& =\text{ }\frac{2}{6}\text{ }+\text{ }\frac{2}{6} \\
& =\text{ }\frac{4}{6} \\
& =\text{ }\frac{2}{3}
\end{align}$
