Question

What is the probability of an impossible event?

• A. \(1\)
• B. \(0.5\)
• C. \(0\)
• D. \(-1\)

Hint:

Remember the three fundamental probability cases:
• Impossible event → \(P = 0\)
• Certain event → \(P = 1\)
• All other events → \(0<P<1\)

Answer 1

The Correct Option is C

Concept:
Probability (\(P\)) is a numerical measure of the likelihood of an event occurring, ranging from \(0\) to \(1\).
Step 1: Understanding the Question:
An impossible event is an event that has no chance of occurring (e.g., rolling a 7 on a standard 6-sided die). We need to state its mathematical probability.
Step 2: Key Formula or Approach:
The probability of any event \(E\) is:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
Step 3: Detailed Solution:
1. For an impossible event, the number of favorable outcomes is exactly \(0\).
2. No matter what the total number of outcomes is, the fraction will be:
\[ P(\text{impossible}) = \frac{0}{n} = 0 \]
Step 4: Final Answer:
The probability of an impossible event is 0.