To determine the probability that Ethan rolls a number less than 3 on a 6-sided number cube, follow these steps:
1. Identify the total number of possible outcomes:
A 6-sided number cube has numbers from 1 to 6. Thus, there are 6 possible outcomes:
[tex]\( \{1, 2, 3, 4, 5, 6\} \)[/tex].
2. Identify the favorable outcomes:
We are interested in rolling a number less than 3. The numbers less than 3 on the cube are 1 and 2. Therefore, there are 2 favorable outcomes:
[tex]\( \{1, 2\} \)[/tex].
3. Calculate the probability:
The probability [tex]\( P \)[/tex] of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore,
[tex]\[
P(\text{rolling a number less than 3}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6}.
\][/tex]
4. Simplify the fraction:
Simplifying the fraction [tex]\( \frac{2}{6} \)[/tex]:
[tex]\[
\frac{2}{6} = \frac{1}{3}.
\][/tex]
Therefore, the probability that Ethan rolls a number less than 3 is [tex]\( \frac{1}{3} \)[/tex].
Thus, the correct answer is:
A. [tex]\( \frac{1}{3} \)[/tex].
