Question

Probability of an impossible event is ____.

• A. 0
• B. 1
• C. -1
• D. \(\infty\)

Hint:

Probability can never be negative and can never exceed 1. If you ever calculate a probability like -0.5 or 1.2, you know immediately that there is an error in the calculation!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Probability is a numerical scale ranging from 0 to 1 that measures the likelihood of an occurrence. An event that has absolutely no chance of happening is categorized as an impossible event.

Step 2: Detailed Explanation:
In probability theory, the probability of any event \( E \), denoted as \( P(E) \), must satisfy the condition \( 0 \le P(E) \le 1 \).
• A Certain Event has a probability of 1 (100% chance).
• An Impossible Event has a probability of 0 (0% chance). For example, the probability of rolling a 7 on a standard six-sided die is 0 because the outcome is not part of the sample space.

Step 3: Final Answer:
The probability of an impossible event is 0.

Answer 2

This question tests the basic property that probability values are bounded between 0 and 1, and asks specifically about the probability assigned to an event that can never occur. Let's evaluate each option:

1. 0: By definition, an impossible event is one that lies outside the sample space, so it has no favorable outcomes at all. Since probability is computed as favorable outcomes divided by total outcomes, an event with zero favorable outcomes must have a probability of exactly 0. This sits at the lower boundary of the axiom \( 0 \le P(E) \le 1 \).
2. 1: A probability of 1 corresponds to a certain event, one guaranteed to happen every single time, which is the exact opposite of an impossible event.
3. -1: Probability can never be negative because it is built from counting outcomes, and counts cannot be negative. A negative value would fall outside the valid range entirely and has no meaning as a probability.
4. \(\infty\): Probability values are always finite and bounded above by 1; an unbounded value cannot represent any event, possible or impossible, on the probability scale.

Only the value 0 satisfies both the boundary condition of the probability axiom and the definition of an event that has no chance of occurring.

Therefore, the correct answer is 0.