An example of an equally likely outcome in math is rolling any specific number on a fair, six-sided die.
In probability, equally likely outcomes are the fundamental building blocks for understanding many experiments. The term "equally likely" simply means that each possible result of a chance event has the exact same probability of occurring.
Understanding Equally Likely Outcomes
As the definition states, equally likely means that each outcome of an experiment occurs with equal probability. This concept is crucial in many areas of mathematics and statistics, especially when calculating probabilities.
Think about simple chance experiments we encounter every day. When these experiments are "fair" or "unbiased," their potential results often fall into the category of equally likely outcomes.
Examples of Equally Likely Outcomes
Let's look at the classic examples provided:
Example 1: Rolling a Fair Six-Sided Die
One of the most common illustrations involves a standard die. According to the definition, if you toss a fair, six-sided die, each face (1, 2, 3, 4, 5, or 6) is as likely to occur as any other face.
This means that when you roll the die, the chance of getting a:
- 1 is the same as the chance of getting a 2.
- 2 is the same as the chance of getting a 3.
- ...and so on, for all faces up to 6.
Each of these six possible outcomes has an equal probability of 1 out of 6 (or 1/6).
Let's visualize this in a simple table:
| Possible Outcome (Face Rolled) | Probability |
|---|---|
| 1 | 1/6 |
| 2 | 1/6 |
| 3 | 1/6 |
| 4 | 1/6 |
| 5 | 1/6 |
| 6 | 1/6 |
As you can see, the probability value (1/6) is identical for every possible outcome.
Example 2: Flipping a Fair Coin
Another clear example is flipping a fair coin. If you toss a fair coin, a Head (H) and a Tail (T) are equally likely to occur.
Assuming the coin is perfectly balanced and won't land on its edge, there are only two possible outcomes: Heads or Tails. Since the coin is fair, neither outcome is favored over the other.
- The probability of getting a Head is equal to the probability of getting a Tail.
- Each outcome has a probability of 1 out of 2 (or 1/2).
These straightforward examples highlight the core idea: in a fair experiment, every potential result has an equal chance of happening.
