Which of the following is a required condition for a discrete probability function?

• A. The sum of all possible probabilities is $1$.
• B. The sum of all possible probabilities is less than $1$.
• C. Probabilities can be greater than $1$.
• D. Each probability can be negative as long as the sum is $1$.

Answer: (A)

Verified step by step guidance

1. Understand that a discrete probability function assigns probabilities to each possible outcome of a discrete random variable.
2. Recall the two main conditions for a valid discrete probability function: (1) Each probability must be between 0 and 1 inclusive, and (2) the sum of the probabilities of all possible outcomes must equal 1.
3. Express the second condition mathematically as: \(\sum_{i} P(X = x_i) = 1\), where \(P(X = x_i)\) is the probability of the \(i\)-th outcome.
4. Recognize that probabilities cannot be negative or greater than 1 because they represent proportions of certainty.
5. Conclude that the required condition is that the sum of all possible probabilities is exactly 1, not less than or greater than 1.