Which of the following is a basic property of probability?

• A. The sum of probabilities of all possible outcomes can exceed 1.
• B. The probability of any event is always between 0 and 1, inclusive.
• C. The probability of any event can be negative.
• D. The probability of an impossible event is always 1.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of probability. Probability is a measure of the likelihood of an event occurring, and it is always expressed as a value between 0 and 1, inclusive. This means that probabilities cannot be negative or exceed 1.
2. Step 2: Review the basic properties of probability. These include: (a) The probability of any event is always between 0 and 1, inclusive. (b) The probability of an impossible event is 0. (c) The probability of a certain event is 1. (d) The sum of probabilities of all possible outcomes in a sample space is 1.
3. Step 3: Evaluate the given options based on the properties of probability. For example, the statement 'The sum of probabilities of all possible outcomes can exceed 1' contradicts the property that the sum of probabilities in a sample space is always 1.
4. Step 4: Analyze the statement 'The probability of any event is always between 0 and 1, inclusive.' This aligns with the fundamental property of probability and is correct.
5. Step 5: Confirm that the other options, such as 'The probability of any event can be negative' and 'The probability of an impossible event is always 1,' are incorrect because they violate the basic principles of probability.