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

A 1/216

B 1/36

C 2/216

D 4/216

Correct Answer: Option A

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

= \(6\times6\times6\times6=6^4\)

n(S) = \(6^4\)

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 = \(\frac{n(X)}{n(S)}=\frac6{6^4}\) = \(\frac1{216}\)