Two dice are thrown simultaneously. What is the probability of getting the face numbers are same?
A
$$\frac{{1}}{{6}}$$
B
$$\frac{{2}}{{3}}$$
C
$$\frac{{4}}{{9}}$$
D
$$\frac{{5}}{{6}}$$
Correct Answer: $$\frac{{1}}{{6}}$$
In a simultaneous throw of two dice, we have n(s) = 6 × 6 = 36Let E = event of getting two numbers are same.
Then E = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
therefore, n(E) = 6
And p(E) = p(getting two numbers are same)
$$\eqalign{ & {\text{p}}\left( {\text{E}} \right) = \frac{{{\text{n}}\left( {\text{E}} \right)}}{{{\text{n}}\left( {\text{S}} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{6}{{36}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{6} \cr} $$
Hence the answer is $$\frac{{1}}{{6}}$$
