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]
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]
