Question:
Two dice are thrown together. The probability of getting the same number on the both dice is .
(a) $\frac{1}{2}$
(b) $\frac{1}{3}$
(C) $\frac{1}{6}$
(d) $\frac{1}{12}$
Solution:
Total number of outcomes = 36.
Getting the same number on both the dice means (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).
Numbers of favourable outcomes = 6.
$\therefore \mathrm{P}($ getting the same number on both dice $)=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$
$=\frac{6}{36}=\frac{1}{6}$
Thus, the probability of getting the same number on both dice is $\frac{1}{6}$.
Hence, the correct answer is option (c).