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

Answer: (B)

Verified step by step guidance

1. Understand that a discrete probability distribution assigns probabilities to each possible outcome of a discrete random variable.
2. Recall the first requirement: each individual probability must be between 0 and 1 inclusive, which can be written as \$0 \leq P(x) \leq 1\( for each outcome \)x$.
3. Recall the second requirement: the sum of all probabilities for all possible outcomes must equal 1, expressed as \(\sum P(x) = 1\).
4. Evaluate the given options by checking if they satisfy both conditions: probabilities between 0 and 1, and total sum equal to 1.
5. Conclude that the correct statement is the one that says each probability is between \$0 \leq P \leq 1$ and the sum of all probabilities is exactly 1.