Which of the following correctly states the two requirements for a discrete probability distribution?

• A. Each probability is negative and the sum of all probabilities is $0$.
• B. Each probability is greater than $1$ and the sum of all probabilities is less than $1$.
• C. Each probability is between $0\le P\le 1$ and the sum of all probabilities is $1$.
• D. Each probability is between $0$ and $1$, but the sum of all probabilities can be any positive number.

Answer: (C)

Verified step by step guidance

1. Recall the definition of a discrete probability distribution: it assigns probabilities to each possible outcome of a discrete random variable.
2. Understand the first requirement: each probability must be between 0 and 1 inclusive, which means for each probability \( P \), it must satisfy \( 0 \leq P \leq 1 \). This ensures probabilities are valid and not negative or greater than 1.
3. Understand the second requirement: the sum of all probabilities for all possible outcomes must equal 1, expressed as \( \sum P_i = 1 \). This ensures the total probability covers all possible outcomes.
4. Evaluate the given options against these two requirements: probabilities must be between 0 and 1, and their sum must be exactly 1.
5. Conclude that the correct statement is: 'Each probability is between \( 0 \leq P \leq 1 \) and the sum of all probabilities is \( 1 \)'.