The probability of rolling an even number on a standard six-sided die is 1/2.
Understanding Probability for a Die Roll
When you roll a standard die, there are a set number of possible outcomes. Probability measures the likelihood of a specific event occurring. It's calculated by comparing the number of ways an event can happen (favorable outcomes) to the total number of possible outcomes.
Possible Outcomes on a Standard Die
A standard die has six faces, each marked with a different number of spots. The possible outcomes when rolling a single die are:
- 1
- 2
- 3
- 4
- 5
- 6
Therefore, the total number of outcomes is 6.
Identifying Even Numbers
An even number is any integer that can be divided by 2 without a remainder. From the possible outcomes on a die, the even numbers are:
- 2
- 4
- 6
These are the favorable outcomes for rolling an even number. There are 3 favorable outcomes.
To visualize the outcomes:
| Die Roll | Type of Number |
|---|---|
| 1 | Odd |
| 2 | Even |
| 3 | Odd |
| 4 | Even |
| 5 | Odd |
| 6 | Even |
The Probability Formula
The fundamental formula for calculating the probability of an event is:
$$P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}$$
Calculating the Probability
Using the formula with the identified outcomes:
- Number of Favorable Outcomes (Even Numbers): 3 (which are 2, 4, 6)
- Total Number of Possible Outcomes: 6 (which are 1, 2, 3, 4, 5, 6)
Now, apply the formula:
$$P(\text{Even Number}) = \frac{3}{6}$$
Representing the Probability
The fraction $\frac{3}{6}$ simplifies to $\frac{1}{2}$. This means that out of every two rolls, on average, one will be an even number.
The probability can be expressed in different forms:
- Fraction: 1/2
- Decimal: 0.5
- Percentage: 50%
In conclusion, when you roll a standard six-sided die, there is an equal chance of rolling an even number as there is an odd number, making the probability precisely 1/2.
