Explanation

(d)
Let $A$be the event of obtaining an even sum and $B$ be the event of obtaining a sum less five.
Then, we have to find $P(A \cup B).$Since, $A,B$ are not mutually exclusive, we have
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$= \frac{18}{36} + \frac{6}{36} - \frac{4}{36}$
$= \frac{5}{9}$
[Since, there are 18 ways to get an even sum and 6 ways to get a sum less than 5 $ie$. (1,3), (3,1), (2,2), (1,2), (2,1),(1,1)
and 4 ways to get an even sum less than 5, $ie$, (1,3), (3,1), (2,2), (1,1).]