Four dice are thrown simultaneously. Find the probability that all of them show the same face.

Answer: Option A

The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
$$\begin{array}{rl}& =6\times 6\times 6\times 6=6^4\\ & n(S)=6^4\end{array}$$
Let X be the event that all dice show the same face.
X = {(1, 1, 1, 1), (2, 2, 2, 2), (3, 3, 3, 3), (4, 4, 4, 4), (5, 5, 5, 5), (6, 6, 6, 6)}
n(X) = 6
Hence required probability,
$$\begin{array}{rl}& =\frac{n(X)}{n(S)}=\frac{6}{6^4}\\ & =\frac{1}{216}\end{array}$$