Which of the following best illustrates the definition of a probability distribution?

• A. A list of all possible outcomes of a random experiment without any probabilities assigned.
• B. A table that shows only the most likely outcome of a random experiment.
• C. A set of numbers that add up to more than $1$.
• D. A table that lists all possible outcomes of a random experiment along with their associated probabilities, where each probability is between $0$ and $1$ and the sum of all probabilities is $1$.

Answer: (D)

Verified step by step guidance

1. Understand that a probability distribution describes how probabilities are assigned to all possible outcomes of a random experiment.
2. Recognize that a probability distribution must include every possible outcome, not just some or the most likely ones.
3. Know that each probability in the distribution must be a number between 0 and 1, inclusive, representing the likelihood of that outcome.
4. Remember that the sum of all probabilities in the distribution must equal exactly 1, ensuring that one of the possible outcomes will occur.
5. Therefore, the best illustration of a probability distribution is a table listing all possible outcomes with their associated probabilities, each between 0 and 1, and summing to 1.