Equally likely

Definition

Equally likely events are those that have the same probability of occurring. In probability theory, this concept is fundamental when considering outcomes in a uniform distribution.

5 Must Know Facts For Your Next Test

1. In a uniform distribution, all intervals of the same length are equally likely.
2. When rolling a fair die, each face (1 through 6) is equally likely to occur with a probability of $\frac{1}{6}$.
3. The sum of probabilities of all equally likely events must equal 1.
4. Equally likely does not mean that the events will occur with equal frequency in every finite sample; it refers to theoretical long-term behavior.
5. In continuous random variables with a uniform distribution over an interval [a, b], any sub-interval of equal length has an equal probability.

Review Questions

• What does it mean for two events to be equally likely?
• Provide an example of equally likely events when rolling a fair six-sided die.
• How does the concept of equally likely apply to continuous random variables in a uniform distribution?

Related terms

Probability: A measure quantifying the likelihood that events will occur, expressed as a number between 0 and 1.

Uniform Distribution: A type of probability distribution where all outcomes are equally likely within a certain range or interval.

Continuous Random Variable: A variable that can take an infinite number of possible values within a given range.