Which of the following is a requirement for a probability distribution?

• A. Each probability can be negative as long as the sum is $1$.
• B. The probability of each outcome must be between $0$ and $1$, inclusive.
• C. The sum of all probabilities must be greater than $1$.
• D. The sum of all probabilities must be less than $1$.

Answer: (B)

Verified step by step guidance

1. Understand that a probability distribution assigns probabilities to all possible outcomes of a random experiment.
2. Recall the first key requirement: each individual probability must be between 0 and 1, inclusive. This means no probability can be negative or greater than 1.
3. Recall the second key requirement: the sum of the probabilities of all possible outcomes must equal exactly 1, representing the certainty that one of the outcomes will occur.
4. Evaluate the given options against these requirements: probabilities cannot be negative, and the sum cannot be less than or greater than 1.
5. Conclude that the correct requirement is that the probability of each outcome must be between 0 and 1, inclusive, and the sum of all probabilities must be exactly 1.