Question:
If \(E'\) is the complementary event of an event \(E\), then which of the following is true?
If \(E'\) is the complementary event of an event \(E\), then which of the following is true?
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Complementary events always add up to 1.
Updated On: Oct 27, 2025
- \(P(E) = P(E')\)
- \(P(E)+P(E')=0\)
- \(P(E)+P(E')=1\)
- None of these
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The Correct Option is C
Solution and Explanation
Step 1: Complement rule.
By definition, \(E+E'=\Omega\) (the sample space).
Step 2: Apply probability axiom.
\[ P(E)+P(E')=P(\Omega)=1 \]
By definition, \(E+E'=\Omega\) (the sample space).
Step 2: Apply probability axiom.
\[ P(E)+P(E')=P(\Omega)=1 \]
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