Question

1. if a single six - sided die is rolled, what is the theoretical probability of rolling a number greater than 4?

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

Explanation:

Step1: Determine total outcomes

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

Step2: Determine favorable outcomes

Numbers greater than 4 on a six - sided die are 5 and 6. So \(n(E) = 2\).

Step3: Use 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:

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