Explanation

(d)
Let $E = \left\{ 2,4,6 \right\}$ [$\because A\ and\ B$ are independent events]
$\therefore\ n(E) = 3$ and $n(S) = 6$
$\therefore\ P(E) = \frac{1}{2}$
Probability of failure $= 1 - \frac{1}{2} = \frac{1}{2}$
$\therefore$ Probability of at least two success
$= P(X = 2) + P(X = 3)$
$= {\ ^{3}C}_{2}\left( \frac{1}{2} \right)^{2}\left( \frac{1}{2} \right)^{1} +^{3}C_{3}\left( \frac{1}{2} \right)^{3}\left( \frac{1}{2} \right)^{0}$
$= \frac{3}{8} + \frac{1}{8} = \frac{1}{2}$