Question

a six - sided die with sides labeled 1 through 6 will be rolled once. each number is equally likely to be rolled. what is the probability of rolling a number greater than 2? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine the total number of outcomes

A standard six - sided die has 6 possible outcomes when rolled, so \(n(S)=6\).

Step2: Determine the number of favorable outcomes

The numbers greater than 2 on a six - sided die are 3, 4, 5, 6. So \(n(A) = 4\).

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\). Substituting the values, we get \(P(A)=\frac{4}{6}\).

Step4: Simplify the fraction

Simplify \(\frac{4}{6}\) by dividing both the numerator and the denominator by 2. \(\frac{4\div2}{6\div2}=\frac{2}{3}\).

Answer:

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