Question

On Marcus's birthday, his father tells him to blindfoldedly choose a cloth in a famous cloth store in downtown. The clothing store sells shirts, pants and jackets. What is the complement of picking a jacket?

• A. Not picking a pant
• B. Not picking a shirt
• C. Picking a shirt or a pant
• D. None of the above

Answer 1

The correct option is C Picking a shirt or a pant

$\underset{–}{\text{Complement of an event}}$

The complement of an event $\text{A}$ is the set of all outcomes in the sample space that are not included in the outcomes of event $\text{A}$. The complement of event A is represented by $\overline{\text{A}}$ (read as A bar).

Suppose, the sample space is $\text{S}$, and an event of picking up a jacket is $\text{E}$. Hence,
$\text{S = {Shirts, Pants, Jackets}}$
$\text{E = {Jacket}}$

$\therefore \overline{\text{E}}=$ The set of all outcomes in the sample space that are not included in the outcomes of event $\text{E}$
$\Rightarrow \overline{\text{E}}=\text{S}-\text{E}$
$\Rightarrow \overline{\text{E}}=\text{{Shirts, Pants, Jackets}}-\text{{Jackets}\}$
$\Rightarrow \overline{\text{E}}=\text{{Shirts, Pants}}$

$\therefore$ Picking a shirt or a pant is the complement of picking a jacket.

Hence, option (c.) is the correct choice.