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. $$\frac{{3}}{{216}}$$
Answer: Option A
Solution(By Examveda Team)
The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:$$\eqalign{ & = 6 \times 6 \times 6 \times 6 = {6^4} \cr & n(S) = {6^4} \cr} $$
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,
$$\eqalign{ & = \frac{{n(X)}}{{n(S)}} = \frac{6}{{{6^4}}} \cr & = \frac{1}{{216}} \cr} $$
Related Questions on Probability
A. $$\frac{{1}}{{2}}$$
B. $$\frac{{2}}{{5}}$$
C. $$\frac{{8}}{{15}}$$
D. $$\frac{{9}}{{20}}$$
A. $$\frac{{10}}{{21}}$$
B. $$\frac{{11}}{{21}}$$
C. $$\frac{{2}}{{7}}$$
D. $$\frac{{5}}{{7}}$$
A. $$\frac{{1}}{{3}}$$
B. $$\frac{{3}}{{4}}$$
C. $$\frac{{7}}{{19}}$$
D. $$\frac{{8}}{{21}}$$
E. $$\frac{{9}}{{21}}$$
What is the probability of getting a sum 9 from two throws of a dice?
A. $$\frac{{1}}{{6}}$$
B. $$\frac{{1}}{{8}}$$
C. $$\frac{{1}}{{9}}$$
D. $$\frac{{1}}{{12}}$$
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