Question

what is the theoretical probability of rolling an even number on a standard six-sided die?

Explanation:

Step1: Identify total possible outcomes

A standard six-sided die has 6 possible outcomes: $1, 2, 3, 4, 5, 6$. So total outcomes $= 6$.

Step2: Identify favorable outcomes

Even numbers on the die are $2, 4, 6$. So favorable outcomes $= 3$.

Step3: Calculate probability

Probability is the ratio of favorable to total outcomes.
$\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{3}{6} = \frac{1}{2}$

Answer:

$\frac{1}{2}$