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 7? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine the total number of outcomes

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

Step2: Determine the number of favorable outcomes

The numbers greater than 7 on a 1 - 12 die are 8, 9, 10, 11, 12. So the number of favorable outcomes \( n(E)=5 \).

Step3: Calculate the probability

The probability formula is \( P(E)=\frac{n(E)}{n(S)} \). Substituting the values, we get \( P(E)=\frac{5}{12} \).

Answer:

\(\frac{5}{12}\)