Three identical dice are rolled. The probability that same number will appear on each of them will be

$\frac{1}{36}$

If three identical dice are rolled then total number of sample points = 6 × 6 × 6 = 216. 

Favourable events (same number appear on each dice) are

(1, 1, 1) (2, 2, 2) ………(6, 6, 6). ∴ Required probability $=\frac{6}{216}=\frac{1}{36}.$