a twelve - sided die with sides labeled 1 through 12 will be rolled once. each number is equally likely to…

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

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

Answer

Explanation:

Step1: Determine total outcomes

The die has 12 sides, so the total number of possible outcomes is 12.

Step2: Determine favorable outcomes

Numbers greater than 4 on a 1 - 12 die are 5, 6, 7, 8, 9, 10, 11, 12. There are 8 such numbers.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P = \frac{8}{12}$.

Step4: Simplify the fraction

$\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}$

Answer:

$\frac{2}{3}$