To find the probability [tex]\( P \)[/tex] that a number rolled on a standard number cube (with faces numbered from 1 to 6) is not a 2, we can follow these steps:
1. Identify Total Possible Outcomes:
- A standard number cube has six faces. Each face represents a possible outcome when the cube is rolled.
- Thus, there are 6 total possible outcomes: [tex]\( 1, 2, 3, 4, 5, \)[/tex] and [tex]\( 6 \)[/tex].
2. Determine Favorable Outcomes:
- We need to count the number of outcomes that are not a 2.
- The outcomes that are not a 2 are: [tex]\( 1, 3, 4, 5, \)[/tex] and [tex]\( 6 \)[/tex].
So, the favorable outcomes are the count of these numbers:
[tex]\[ 1, 3, 4, 5, 6 \][/tex]
There are 5 favorable outcomes.
3. Set Up the Probability Formula:
- Probability [tex]\( P \)[/tex] is defined as the ratio of favorable outcomes to the total possible outcomes.
- The formula for probability is:
[tex]\[
P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}
\][/tex]
4. Calculate the Probability:
- Plug in the values:
[tex]\[
P = \frac{5}{6}
\][/tex]
Therefore, the probability [tex]\( P \)[/tex] that the number rolled is not a 2 is:
[tex]\[
P = \frac{5}{6}
\][/tex]
Thus, the correct answer is [tex]\(\frac{5}{6}\)[/tex].
