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

The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:

=  $6*6*6*6=64$

n(S) =  $64$

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 =  $\frac{n\left(X\right)}{n\left(S\right)}=\frac{6}{6}$ = $\frac{1}{216}$