Question

you roll a fair die. what is the probability that you roll an even number?

Explanation:

Step1: Identify total outcomes

A fair die has 6 sides, so total outcomes $n(S)=6$.

Step2: Identify favorable outcomes

Even - numbered faces on a die are 2, 4, 6. So favorable outcomes $n(E)=3$.

Step3: Calculate probability

The probability formula is $P(E)=\frac{n(E)}{n(S)}$. Substituting values, we get $P(E)=\frac{3}{6}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$