Let's find the probability of rolling a 5 with a single roll of a die.
1. Understand the Problem:
A standard die has 6 faces, numbered from 1 to 6.
2. Determine the Total Number of Outcomes:
When rolling a die, there are 6 possible outcomes (the die can land on 1, 2, 3, 4, 5, or 6).
3. Identify the Desired Outcome:
We are interested in the outcome where the die shows a 5. There is exactly 1 desired outcome.
4. Calculate the Probability:
The probability of a specific outcome when rolling a die is the number of desired outcomes divided by the total number of outcomes.
Using the formula:
[tex]\[
P(\text{specific outcome}) = \frac{\text{Number of desired outcomes}}{\text{Total number of outcomes}}
\][/tex]
For rolling a 5:
[tex]\[
P(5) = \frac{1}{6}
\][/tex]
5. Convert the Fraction to a Decimal:
To express the probability as a decimal rounded to 3 decimal places, we observe that:
[tex]\[
\frac{1}{6} \approx 0.167
\][/tex]
So, the probability [tex]\( P(5) \)[/tex] of rolling a 5 on a single roll of a die, rounded to 3 decimal places, is:
[tex]\[
P(5) = 0.167
\][/tex]
