Mathematics

Problem

Which of the following correctly states the complement rule for an event

E

in probability? a)

P(E)\,P(E^{c}) = 1

P(E)+P(E^{c}) = 1

\dfrac{P(E)}{P(E^{c})} = 1

P(E)-P(E^{c}) = 1

Intuitive explanation

The complement rule is about recognizing that an event and its opposite must cover all possibilities. If $E$ is any event, then $E$ and "not $E$ " are mutually exclusive and exhaustive—they can't both happen, but one of them always does. This means their probabilities must add up to exactly 1, giving you a powerful way to find $P(E)$ by calculating $P(\text{not } E)$ instead, which is often much simpler.

Intuitive explanation

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