Question

a twelve - sided die with sides labeled 1 through 12 will be rolled once. each number is equally likely to be rolled. what is the probability of rolling a number less than 9? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine total outcomes

A 12 - sided die has 12 possible outcomes (1 to 12), so total outcomes \( n = 12 \).

Step2: Find favorable outcomes

Numbers less than 9 are 1, 2, 3, 4, 5, 6, 7, 8. So number of favorable outcomes \( m=8 \).

Step3: Calculate probability

Probability \( P=\frac{m}{n}=\frac{8}{12} \), simplify by dividing numerator and denominator by 4: \( \frac{8\div4}{12\div4}=\frac{2}{3} \).

Answer:

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