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

A. $\frac{1}{216}$

B. $\frac{1}{36}$

C. $\frac{4}{216}$

D. $\frac{3}{216}$

Solution:

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

\begin{aligned} = 6 \times 6 \times 6 \times 6 = 6^{4} \\ n (S) = 6^{4} \end{aligned}

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{aligned} = \frac{n (X)}{n (S)} = \frac{6}{6^{4}} \\ = \frac{1}{216} \end{aligned}

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