Three identical dice are rolled. The probability that same number appears on them, is

$\frac{1}{36}$

The total number of elementary events associated to the random experiment of throwing three dice simultaneously is $6^3$.

Same number appears on three dice in ${^6C}_1$ ways.

∴ Probability of getting the same number= $\frac{^6C_1}{6^3}=\frac{1}{6^2}=\frac{1}{36}$