Question

What is the probability that one roll of a fair six-sided die will result in an even number?

Short answer

The probability is \(\frac{1}{2}\).

Step-by-step solution

Identify Total Possible Outcomes

A fair six-sided die has six faces. Each face has a unique number from 1 to 6. Therefore, the total number of possible outcomes is 6.

Identify Favorable Outcomes

The favorable outcomes for rolling an even number on a six-sided die are the numbers 2, 4, and 6. There are 3 favorable outcomes.

Calculate the Probability

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability is \(\frac{3}{6} \).

Simplify the Fraction

Simplify the fraction \(\frac{3}{6}\) to get \(\frac{1}{2}\).

Key concepts

fair six-sided die

A fair six-sided die is a cube with numbers from 1 to 6 on its faces. Each number appears only once.
The key feature of a fair die is that each face has an equal chance of landing face up.
That means the probability of landing on any given number is always 1 out of 6.
This equal probability ensures fairness in games and statistical experiments.

favorable outcomes

In probability, favorable outcomes are the specific results that match the event you are measuring.
For instance, if you want to roll an even number on a six-sided die, only certain numbers are favorable.
These numbers are 2, 4, and 6 because they meet the condition of being even.
Therefore, there are 3 favorable outcomes in this scenario.

total possible outcomes

Total possible outcomes are all the possible results that could happen in an experiment.
For a six-sided die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6.
Understanding the total number of possible outcomes is crucial for calculating probabilities.
It's the denominator in the probability formula, representing the whole set of results.

simplification of fractions

When you calculate probability, you often end up with a fraction. Simplification makes this fraction easier to understand and use.
For example, if you have \(\frac{3}{6}\), you can simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 3 in this case.
So, \(\frac{3}{6} = \frac{1}{2}\).
Simplifying fractions helps you better interpret the probability and communicate it clearly.