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 less than 5?
Write your answer as a fraction in simplest form.

Answer 1

To determine the probability of rolling a number less than 5 on a six-sided die, we first identify the favorable outcomes. The numbers on the die are 1, 2, 3, 4, 5, and 6. The numbers that are less than 5 are 1, 2, 3, and 4.

So, the favorable outcomes are:
- 1
- 2
- 3
- 4

This gives us a total of 4 favorable outcomes. The total number of possible outcomes when rolling the die is 6 (since there are 6 sides).

The probability \( P \) of rolling a number less than 5 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:

\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{6}
\]

Next, we simplify the fraction \( \frac{4}{6} \):

\[
\frac{4}{6} = \frac{2}{3}
\]

Thus, the probability of rolling a number less than 5 is:

\[
\boxed{\frac{2}{3}}
\]