Sure, let's solve the problem step-by-step!
We need to figure out the probability of rolling a 1 or a 4 on a number cube (also known as a die) with sides labeled from 1 to 6.
1. Identify the Total Number of Outcomes:
A standard number cube has 6 faces. Each face represents one outcome when the cube is rolled. Therefore, the total number of possible outcomes when rolling the cube is 6.
2. Identify the Favorable Outcomes:
The question asks for the probability of rolling either a 1 or a 4. Thus, the favorable outcomes are those where the number showing on the cube is either 1 or 4. This gives us 2 favorable outcomes (rolling a 1 and rolling a 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 possible outcomes. So,
[tex]\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{6}
\][/tex]
4. Simplify the Fraction:
The fraction [tex]\(\frac{2}{6}\)[/tex] can be simplified 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]
So, the probability of rolling a 1 or a 4 on a number cube labeled 1 through 6 is [tex]\(\frac{1}{3}\)[/tex].
Therefore, the correct answer is:
B. [tex]\(\frac{1}{3}\)[/tex]
