To determine the probability of rolling an even number two times on a fair six-sided die, we first identify the even numbers on the die, which are 2, 4, and 6. Therefore, there are 3 even numbers out of a total of 6 possible outcomes.
The probability of rolling an even number on a single roll of the die is:
\[ P(\text{even number}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \]
Since the rolls are independent events, the probability of rolling an even number on both rolls is:
\[ P(\text{even on both rolls}) = P(\text{even on first roll}) \times P(\text{even on second roll}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
Thus, the probability of rolling an even number on both rolls is \(\frac{1}{4}\) or 25%.
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