Question

the probability of rolling a number less than 5 on a six - sided die is:
a. $\frac{1}{2}$
b. $\frac{2}{3}$
c. $\frac{1}{6}$
d. $\frac{5}{6}$

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 less than \(5\) are \(1,2,3,4\), so \(n(E) = 4\).

Step3: Calculate probability

Probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substitute \(n(E) = 4\) and \(n(S)=6\), we get \(P(E)=\frac{4}{6}=\frac{2}{3}\).

Answer:

B. \(\frac{2}{3}\)