Question

If \(E'\) is the complementary event of an event \(E\), then which of the following is true?

• A. \(P(E) = P(E')\)
• B. \(P(E)+P(E')=0\)
• C. \(P(E)+P(E')=1\)
• D. None of these

Hint:

Complementary events always add up to 1.

Answer 1

The Correct Option is C

Step 1: Complement rule.
By definition, \(E+E'=\Omega\) (the sample space).
Step 2: Apply probability axiom.
\[ P(E)+P(E')=P(\Omega)=1 \]