Question

Notation When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do $P\left(A\right)$and $P\left(\overline{A}\right)$represent ?

Short answer

$P\left(A\right)$represents the probability of selecting an adult having blue eyes.

$P\left(\overline{A}\right)$represents the probability of selecting an adult without blue eyes.

Step-by-step solution

Given information

A is the event of selecting an adult with blue eyes.

Complementary event

In the probability theory, if A is a given event, then $P\left(A\right)$is the probability of occurrence of event A and $P\left(\overline{A}\right)$is the probability of the complementary event.

Here,is called the complement of event A,which is not getting A.

Interpretation in terms of the given event

Here, A is the event of selecting an adult who has blue eyes.

Therefore, $\overline{A}$is the complement of event A.

Thus, $\overline{A}$is the event of selecting an adult who does not have blue eyes.

• P(A) is the probability of selecting a random adult with blue eyes.
• $P\left(\overline{A}\right)$is the probability of selecting a random adult who does not have blue eyes.