Answer :
To determine the probability that Ethan rolls a number less than 3 on a 6-sided number cube, let's break down the problem step by step:
1. Identify the Total Number of Possible Outcomes:
- A 6-sided number cube has 6 faces, each with a distinct number from 1 to 6.
- Therefore, the total number of possible outcomes when rolling the cube is 6.
2. Identify the Favorable Outcomes:
- We are interested in rolling a number that is less than 3.
- The numbers on the cube that are less than 3 are 1 and 2.
- Hence, there are 2 favorable outcomes.
3. Calculate the Probability:
- Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- Therefore, the probability \( P \) of rolling a number less than 3 is given by:
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{6} \][/tex]
4. Simplify the Fraction:
- Simplify \(\frac{2}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \][/tex]
Therefore, the probability that Ethan rolls a number less than 3 is \(\frac{1}{3}\).
The correct answer is:
D. [tex]\(\frac{1}{3}\)[/tex]
1. Identify the Total Number of Possible Outcomes:
- A 6-sided number cube has 6 faces, each with a distinct number from 1 to 6.
- Therefore, the total number of possible outcomes when rolling the cube is 6.
2. Identify the Favorable Outcomes:
- We are interested in rolling a number that is less than 3.
- The numbers on the cube that are less than 3 are 1 and 2.
- Hence, there are 2 favorable outcomes.
3. Calculate the Probability:
- Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- Therefore, the probability \( P \) of rolling a number less than 3 is given by:
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{6} \][/tex]
4. Simplify the Fraction:
- Simplify \(\frac{2}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \][/tex]
Therefore, the probability that Ethan rolls a number less than 3 is \(\frac{1}{3}\).
The correct answer is:
D. [tex]\(\frac{1}{3}\)[/tex]
