Sample space: 36 outcomes, each represented by an ordered pair denoting the result of the first and second die rolls.
The sample space for rolling two distinguishable, fair, six-sided dice consists of all possible outcomes when rolling both dice.
Each die has six sides, so the total number of outcomes is 6×6=36.
The sample space can be represented as a set of ordered pairs, where each element represents the outcome of each die roll.
For instance, if we denote the outcomes as (first die, second die), the sample space can be listed as:
{(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)}