The probability of obtaining an even prime number on each dice when a pair of dice is rolled is

(i) 0

(ii) $\cfrac{1}{3}$

(iii) $\cfrac{1}{{12}}$

(iv) $\cfrac{1}{{36}}$

Option D is correct

When a pair ofdice is rolled once,

the sample space contains $6 \times 6 = 36$ equally
likely simple events

$\therefore$ $S = {\left\{ {\begin{array}{cccccccccccccccccccc}{(1,1)}& \ldots &{(1,6)}\\ \vdots & \ldots & \vdots \\{(6,1)}& \ldots &{(6,6)}\end{array}} \right\}_{6 \times 6 = 36}}$

Let $E$ be the event that even prime number comes on each dice,

then sample points for $E$

is {(2,2)}

$\therefore$ Required probability $P(E) = \cfrac{1}{{36}}$

( is the only favourable outcome)