Question

Finding Complements. In Exercises 5–8, find the indicated complements.

Flying In a Harris survey, adults were asked how often they typically travel on commercial flights, and it was found that $P\left(N\right)=0.330$, where N denotes a response of “never.” What does $P\left(\overline{N}\right)$represent, and what is its value?

Short answer

$P\left(\overline{N}\right)$represents the probability of a response other than “never.” Its value is equal to 0.67.

Step-by-step solution

Given information

The probability of the response “never” is denoted by and is equal to 0.330.

Express the Complementary events

Let E be an event. Then,$\overline{E}$denotes all the outcomes that do not result in E.

In this case, $\overline{E}$is called thecomplementary event of E.

The sum of the probabilities of E and its complement is equal to 1.

$P\left(E\right)+P\left(\overline{E}\right)=1$

Compute the probability for the complementary event 

Let N be the event of getting a response of “never.”

Then, $\overline{N}$is the event of getting a response other than “never.”

The probability of getting a response other than “never” is calculated as follows:

$$\begin{gathered} P\left(\overline{N}\right)=1-P\left(N\right) \\ =1-0.330 \\ =0.670 \end{gathered}$$

Thus, $P\left(\overline{N}\right)$is equal to 0.67.