Multiple Choice
In the context of probability, which statement best describes a as compared to a ?
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4. Probability
Basic Concepts of Probability
Multiple Choice
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 .
B
Each probability is between and , but the sum can be any positive number.
C
Each probability is greater than and the sum of all probabilities is less than .
D
Each probability is between and the sum of all probabilities is .
Verified step by step guidance1
Understand that a discrete probability distribution assigns probabilities to each possible outcome of a discrete random variable.
Recall the first requirement: each probability must be between 0 and 1 inclusive, which can be written as \(0 \leq P(x) \leq 1\) for each outcome \(x\).
Recall the second requirement: the sum of all probabilities for all possible outcomes must equal 1, expressed as \(\sum P(x) = 1\).
Evaluate the given options by checking if they satisfy both conditions: probabilities between 0 and 1, and total sum equal to 1.
Conclude that the correct statement is: 'Each probability is between \(0 \leq P \leq 1\) and the sum of all probabilities is 1.'
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