Question

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

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

Explanation:

Step1: Determine total outcomes

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

Step2: Determine favorable outcomes

Even numbers on a die are \(2,4,6\), so there are 3 favorable outcomes.

Step3: Calculate probability

The probability formula is \(P=\frac{\text{favorable outcomes}}{\text{total outcomes}}\). So \(P = \frac{3}{6}=\frac{1}{2}\).

Answer:

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