A doublet refers to a situation where both dice show the same number. When two dice are rolled, there are a total of \(6 \times 6 = 36\) possible outcomes. The doublets are:
\((1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)\)
Thus, there are 6 favorable outcomes for getting a doublet. Therefore, the probability is:
\[ \frac{6}{36} = \frac{1}{6} \]
So, the correct answer is \(\frac{1}{6}\).