The probability of an event is determined a follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}[/tex]We shall begin with the probability of selecting an even number as shown below;
[tex]\begin{gathered} P\lbrack\text{even\rbrack}=\frac{6}{12} \\ P\lbrack\text{even\rbrack}=\frac{1}{2} \end{gathered}[/tex]Next we shall calculate the probability of selecting a number less than 5 as shown below;
[tex]\begin{gathered} P\lbrack\text{less than 5\rbrack=}\frac{4}{12} \\ P\lbrack\text{less than 5\rbrack=}\frac{1}{3} \end{gathered}[/tex]The probability of event A OR event B occuring is calculated a follows;
[tex]\begin{gathered} P\lbrack A\rbrack\text{ OR P\lbrack{}B\rbrack=P\lbrack{}A\rbrack+P\lbrack{}B\rbrack} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{1}{2}+\frac{1}{3} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{3+2}{6} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{5}{6} \end{gathered}[/tex]The probability of selecting an even number or a number less than 5 is therefore
[tex]\frac{5}{6}[/tex]The correct answer is option A