Question

a single fair eight - sided die is rolled. find the probability of getting a number less than 5.
the probability is
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine the total number of outcomes

When rolling an eight - sided die, the total number of possible outcomes \(n(S)\) is \(8\) (the numbers \(1,2,3,4,5,6,7,8\)).

Step2: Determine the number of favorable outcomes

The numbers less than \(5\) are \(1,2,3,4\). So the number of favorable outcomes \(n(E)\) is \(4\).

Step3: Use the probability formula

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 4\) and \(n(S)=8\) into the formula, we get \(P(E)=\frac{4}{8}\). Simplifying \(\frac{4}{8}\) by dividing both the numerator and the denominator by \(4\), we have \(P(E)=\frac{1}{2}\).

Answer:

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