Ethan rolls a 6-sided number cube. What is the probability that he gets a number less than 4?

A. [tex]\frac{2}{3}[/tex]
B. [tex]\frac{1}{3}[/tex]
C. [tex]\frac{1}{6}[/tex]
D. [tex]\frac{1}{2}[/tex]



Answer :

To determine the probability that Ethan rolls a number less than 4 on a 6-sided number cube, let's break down the problem step-by-step.

1. Identify Total Possible Outcomes:
A standard 6-sided number cube has faces numbered 1 through 6, so there are 6 possible outcomes in total when the cube is rolled.

2. Identify Favorable Outcomes:
We need to determine the outcomes that are less than 4. The numbers less than 4 on a 6-sided cube are 1, 2, and 3. Thus, there are 3 favorable outcomes.

3. Calculate the Probability:
The probability of an event is given by the formula:
[tex]\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \][/tex]
Substituting the values we determined:
[tex]\[ \text{Probability} = \frac{3}{6} \][/tex]

4. Simplify the Fraction:
[tex]\[ \frac{3}{6} = \frac{1}{2} \][/tex]

Therefore, the probability that Ethan rolls a number less than 4 is [tex]\(\frac{1}{2}\)[/tex].

So, the correct answer from the given options is:
D. [tex]\(\frac{1}{2}\)[/tex]