Question

The complement of an event $\text{E}$ is the

• A. set of outcomes in sample space which belong to event $\text{E}$.
• B. set of outcomes in sample space which do not belong to event $\text{E}$.
• C. set of outcomes in sample space which belong to event ${\text{E}}^2$.
• D. None of the above

Answer 1

The correct option is B set of outcomes in sample space which do not belong to event $\text{E}$.

The complement of an event $\text{E}$ is the set of all outcomes in the sample space that are not included in the outcomes of event $\text{E}$.

In other words, complement of an event $\text{E}$ is the occurrence of all the outcomes that are not favorable to the event $\text{E}$.

$\underset{–}{\text{Example}}$:
Tom defines an event $\text{E}$ as rolling an even number in a fair die.

For rolling a fair die, sample Space= $\text{S}=\{1,2,3,4,5,6\}$.

Favorable outcomes of the event $\text{E}=\{2,4,6\}$

Now, the compliment of event $\text{E}$= $\overline{\text{E}}$ = Set of outcomes in sample space which are not included in the event $\text{E}=\{1,3,5\}$.

$\underset{–}{\text{Remark:}}$

$\overline{\text{E}}=\text{S}-\text{E}$, Where $\text{S, E}$ and $\overline{\text{E}}$ are sample space, event and compliment of event, respectively.