Question:
If an event cannot occur, then its probability is:
If an event cannot occur, then its probability is:
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A certain event has probability \(1\), while an impossible event has probability \(0\).
Updated On: Jun 16, 2026
- \(1\)
- \(\frac{4}{3}\)
- \(\frac{1}{2}\)
- \(0\)
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The Correct Option is D
Solution and Explanation
Concept:
Probability always satisfies
\[
0\le P(E)\le 1.
\]
An event that cannot occur is called an impossible event and is represented by the empty set \(\varnothing\).
Its probability is
\[
P(\varnothing)=0.
\]
Step 1: Identify the type of event. The event described in the question cannot occur. Therefore, it is an impossible event.
Step 2: Apply the probability rule. For an impossible event, \[ P(\varnothing)=0. \] Hence, \[ P(E)=0. \] Conclusion: \[ \boxed{0} \] Hence, the correct answer is Option (D).
Step 1: Identify the type of event. The event described in the question cannot occur. Therefore, it is an impossible event.
Step 2: Apply the probability rule. For an impossible event, \[ P(\varnothing)=0. \] Hence, \[ P(E)=0. \] Conclusion: \[ \boxed{0} \] Hence, the correct answer is Option (D).
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