A probability model in which all outcomes are equally likely is called a uniform distribution. In a uniform distribution, each possible outcome has the same probability of occurring.
For example, when rolling a fair six-sided die, the probability of rolling any one of the six numbers (1 through 6) is equal, specifically \( \frac{1}{6} \). Similarly, if you were to randomly select an outcome from a finite set where each option has the same chance of being chosen (like picking a card from a well-shuffled standard deck of cards), it would also follow a uniform distribution.
Mathematically, if there are \( n \) equally likely outcomes, the probability of any specific outcome occurring is given by:
\[ P(\text{outcome}) = \frac{1}{n} \]
Uniform distributions can be continuous as well, such as when selecting a number from an interval \([a, b]\) where the probability density function is constant over that interval. In this case, the probability density function \( f(x) \) is defined as:
\[ f(x) = \frac{1}{b - a} \quad \text{for } a \leq x \leq b \]
Thus, all outcomes in the interval have the same likelihood.