Question

use the theoretical method to determine the probability of the given outcome or event. assume that the die is fair. rolling a single six - sided die and getting a 2 or 4. the probability rolling a single six - sided die and getting a 2 or 4 is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine total number of outcomes

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

Step2: Determine number of favorable outcomes

The favorable outcomes (getting a \(2\) or \(4\)) are \(n(E) = 2\) (the outcomes \(2\) and \(4\)).

Step3: Use the probability formula

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

Answer:

\(\frac{1}{3}\)