Question

Two dice are thrown simultaneously. The probability of getting a pair of aces is
(a) 1/36
(b) 1/3
(c) 1/6
(d) none of these

Answer 1

Sample space when two dice are rolled is

$S\left\{\begin{array}{l}\left(1,1\right)\left(1,2\right)\left(1,3\right)\left(1,4\right)\left(1,5\right)\left(1,6\right)\\ \left(2,1\right)\left(2,2\right)...........\left(2,6\right)\\ \left(3,1\right)\\ \left(4,1\right)\\ \left(5,1\right)\\ \left(6,1\right).......\left(6,6\right)\end{array}\right.$
i.e. number of element in S is 36.
Number of favourable outcome i.e. both aces is 1 i.e. {(1, 1)}

$$\begin{gathered} \therefore \mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{pair}\mathrm{of}\mathrm{aces}\mathrm{is}\frac{\mathrm{no}.\mathrm{of}\mathrm{favourable}\mathrm{outcome}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ \mathrm{i}.\mathrm{e}.\frac{1}{36} \end{gathered}$$
Hence, the correct answer is option A.