Question

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

a. $\frac{1}{2}$
b. $\frac{1}{3}$
c. $\frac{2}{3}$
d. $\frac{3}{6}$

Explanation:

Step1: Determine total outcomes

A six - sided die has \(n(S)=6\) possible outcomes (\(1,2,3,4,5,6\)).

Step2: Determine favorable outcomes

Even numbers on a die are \(2,4,6\), so \(n(E) = 3\).

Step3: Use probability formula

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

Answer:

A. \(\frac{1}{2}\)