Which of the following statements best describes a probability distribution?

• A. It assigns a probability to each possible outcome in a sample space such that the probabilities are between $0$ and $1$ and the total probability sums to $1$.
• B. It lists all possible outcomes of an experiment without assigning any probabilities.
• C. It is a function that always assigns a probability greater than $1$ to at least one outcome.
• D. It describes only the most likely outcome of a random experiment.

Answer: (A)

Verified step by step guidance

1. Understand that a probability distribution is a function that assigns probabilities to each possible outcome in a sample space.
2. Recall the two key properties of a probability distribution: each probability must be between 0 and 1 inclusive, and the sum of all probabilities must equal 1.
3. Recognize that simply listing outcomes without probabilities does not constitute a probability distribution because it lacks the assignment of probabilities.
4. Note that assigning a probability greater than 1 to any outcome violates the fundamental rules of probability, so such a function cannot be a probability distribution.
5. Understand that a probability distribution describes the probabilities of all possible outcomes, not just the most likely one.