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 greater than 10? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine the total number of possible outcomes

The die has 12 sides, so the total number of possible outcomes is \( n = 12 \).

Step2: Determine the number of favorable outcomes

Numbers greater than 10 on a 1 - 12 die are 11 and 12. So the number of favorable outcomes is \( m=2 \).

Step3: Calculate the probability

The probability formula is \( P=\frac{m}{n} \). Substituting \( m = 2 \) and \( n = 12 \), we get \( P=\frac{2}{12}=\frac{1}{6} \).

Answer:

\(\frac{1}{6}\)