Answer :
To determine the probability that Ethan rolls a number greater than 2 on a 6-sided number cube, we can follow these steps:
1. Identify the Total Number of Outcomes:
Since a standard number cube (die) has 6 faces, the total number of possible outcomes when Ethan rolls the cube is 6. These outcomes are: \(1, 2, 3, 4, 5,\) and \(6\).
2. Identify the Favorable Outcomes:
We need to find the outcomes where the number rolled is greater than 2. The numbers greater than 2 on a 6-sided cube are: \(3, 4, 5,\) and \(6\). Therefore, the number of favorable outcomes is 4.
3. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability \(P\) that Ethan rolls a number greater than 2 can be calculated as:
[tex]\[ P(\text{number greater than 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
Substituting the numbers from our steps:
[tex]\[ P(\text{number greater than 2}) = \frac{4}{6} \][/tex]
4. Simplify the Fraction:
Simplify the fraction \(\frac{4}{6}\) to its lowest terms. Both the numerator and the denominator can be divided by their greatest common divisor, which is 2:
[tex]\[ \frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \][/tex]
Therefore, the probability that Ethan rolls a number greater than 2 on a 6-sided number cube is \(\frac{2}{3}\).
Thus, the correct answer is:
B. [tex]\(\frac{2}{3}\)[/tex]
1. Identify the Total Number of Outcomes:
Since a standard number cube (die) has 6 faces, the total number of possible outcomes when Ethan rolls the cube is 6. These outcomes are: \(1, 2, 3, 4, 5,\) and \(6\).
2. Identify the Favorable Outcomes:
We need to find the outcomes where the number rolled is greater than 2. The numbers greater than 2 on a 6-sided cube are: \(3, 4, 5,\) and \(6\). Therefore, the number of favorable outcomes is 4.
3. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability \(P\) that Ethan rolls a number greater than 2 can be calculated as:
[tex]\[ P(\text{number greater than 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
Substituting the numbers from our steps:
[tex]\[ P(\text{number greater than 2}) = \frac{4}{6} \][/tex]
4. Simplify the Fraction:
Simplify the fraction \(\frac{4}{6}\) to its lowest terms. Both the numerator and the denominator can be divided by their greatest common divisor, which is 2:
[tex]\[ \frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \][/tex]
Therefore, the probability that Ethan rolls a number greater than 2 on a 6-sided number cube is \(\frac{2}{3}\).
Thus, the correct answer is:
B. [tex]\(\frac{2}{3}\)[/tex]
