Explanation

(d)
Let $A =$ Event of getting even number on first die
={(2, 1)………..(2, 6)
(4, 1)…………..(4, 6)
(6, 1)…………...(6, 6)}
and $B =$ Events of getting a sum of 8
$= \left\{ (2,\ 6),(3,\ 5),\ (4,\ 4),\ (5,\ 3),\ (6,\ 2) \right\}$
$A \cap B = \left\{ (2,\ 6),\ (4,\ 4),\ (6,\ 2) \right\}$
$\therefore\ n(A) = 18,\ n(B) = 5,\ n(A \cap B) = 3$
$\Rightarrow \ n(A \cup B) = 18 + 5 - 3 = 20$
$\therefore\ P(A \cup B) = \frac{n(A \cup B)}{n(S)} = \frac{20}{36} = \frac{5}{9}$