Clearly, $ n \left(S\right)$ = $(6 \times 6)$ = 36.

Let E = Event that the sum is a prime number.

Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
      (5, 2), (5, 6), (6, 1), (6, 5) }

$\therefore n \left(E\right)$ = 15.

$\therefore P\left(E\right)$ =$ \dfrac{n(E)}{n(S)} $=$ \dfrac{15}{36} $=$ \dfrac{5}{12} $.