Let’s address these probability questions one by one with detailed steps:
1. Probability of rolling a 5 on a number cube:
A standard number cube (also known as a die) has faces numbered from 1 to 6. To determine the probability of rolling a 5, we need to consider the following:
- Number of favorable outcomes: There is only one favorable outcome, which is rolling a 5.
- Total number of possible outcomes: There are 6 possible outcomes corresponding to the 6 faces of the die (1, 2, 3, 4, 5, and 6).
The formula for probability is given by:
[tex]\[
P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Applying this to our problem:
[tex]\[
P(\text{rolling a 5}) = \frac{1}{6}
\][/tex]
Therefore, the probability of rolling a 5 on a number cube is [tex]\(\frac{1}{6}\)[/tex].
2. Probability of rolling a number greater than 6 on a number cube:
Again, a standard number cube has faces numbered from 1 to 6. Here, we need to determine if there are any numbers that are greater than 6 on the cube.
- Number of favorable outcomes: There are no numbers greater than 6 on a standard number cube.
- Total number of possible outcomes: The number cube still has 6 possible outcomes (1, 2, 3, 4, 5, and 6).
Since there are no favorable outcomes, the probability is calculated as:
[tex]\[
P(\text{number greater than 6}) = \frac{0}{6}
\][/tex]
Simplifying this fraction:
[tex]\[
P(\text{number greater than 6}) = 0
\][/tex]
Therefore, the probability of rolling a number greater than 6 on a number cube is [tex]\(0\)[/tex], indicating that it is impossible.
