You roll a standard number cube. Find [tex]P(\text{number is not } 2)[/tex].

A. [tex]\frac{1}{2}[/tex]
B. [tex]\frac{5}{6}[/tex]
C. [tex]\frac{1}{6}[/tex]
D. [tex]\frac{2}{3}[/tex]



Answer :

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].