Question

1. what is the probability of rolling a number greater than 4 on a standard six - sided die?

a. $\frac{1}{3}$
b. $\frac{1}{6}$
c. $\frac{1}{4}$
d. $\frac{1}{2}$

Explanation:

Step1: Determine total number of outcomes

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

Step2: Determine number of 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:

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