To make it perfectly clear, consider the sample space for rolling a die twice.

**(1, 1)** (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)  
(2, 1) **(2, 2)** (2, 3) (2, 4) (2, 5) (2, 6)  
(3, 1) (3, 2) **(3, 3)** (3, 4) (3, 5) (3, 6)  
(4, 1) (4, 2) (4, 3) **(4, 4)** (4, 5) (4, 6)  
(5, 1) (5, 2) (5, 3) (5, 4) **(5, 5)** (5, 6)  
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) **(6, 6)**  

There are 36 equally likely possible outcomes, 6 of which define the event "rolling the same number two times in a row". Then, the probability of this event occurring is $\frac{6}{36}$, which is equal to $\frac{1}{6}$.