Question

if a single six - sided die is rolled, what is the theoretical probability of rolling a number greater than 4? a. $\frac{2}{3}$ b. $\frac{1}{3}$ c. $\frac{1}{6}$ d. $\frac{1}{2}$

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

Numbers greater than \(4\) on a die are \(5\) and \(6\), so \(n(E) = 2\).

Step3: Calculate probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting values: \(P(E)=\frac{2}{6}=\frac{1}{3}\).

Answer:

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