Final Answer:
The given statement "The sum of two rolled dice is always even." is false.
Explanation:
When rolling a standard six-sided die, the possible outcomes range from 1 to 6. Considering two dice, the lowest possible sum is 1 (when both dice show 1), and the highest is 12 (when both dice show 6). To determine if the sum is even or odd, we analyze the possible outcomes. Among the 36 possible combinations (6 outcomes for the first die multiplied by 6 outcomes for the second die), there are 18 combinations resulting in an even sum and 18 combinations resulting in an odd sum.
To understand this conceptually, let's consider the nature of even and odd numbers. When you add two even numbers or two odd numbers together, the sum is always even.
However, when you add an even number to an odd number, the result is always odd. In the case of two dice, each die has an equal chance of landing on an even or odd number, resulting in an equal number of even and odd sums when combined. Hence, the statement that the sum of two rolled dice is always even is false, as there are an equal number of possibilities for both even and odd sums.