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Chapter 4: Q7 (page 156)

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 PN=0.330, where N denotes a response of “never.” What does PN¯represent, and what is its value?

Short Answer

Expert verified

PN¯represents the probability of a response other than “never.” Its value is equal to 0.67.

Step by step solution

01

Given information

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

02

Express the Complementary events

Let E be an event. Then,E¯denotes all the outcomes that do not result in E.

In this case, E¯is called thecomplementary event of E.

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

PE+PE¯=1

03

Compute the probability for the complementary event 

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

Then, N¯is the event of getting a response other than “never.”

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

PN¯=1-PN=1-0.330=0.670

Thus, PN¯is equal to 0.67.

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Most popular questions from this chapter

Penicillin “Who discovered penicillin: Sean Penn, William Penn, Penn Jillette, Alexander Fleming, or Louis Pasteur?” If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming?

Complements and the Addition Rule Refer to the table used for Exercises 9–20. Assume that one order is randomly selected. Let A represent the event of getting an order from McDonald’s and let B represent the event of getting an order from Burger King. Find PAorB¯, find PA¯orB¯, and then compare the results. In general, does PAorB¯= PA¯orB¯?

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a. = (0.95)(0.95)(0.95) = 0.857

b. P(A) = 1 - (0.95)(0.95)(0.95) = 0.143

c. P(A) = (0.05)(0.05)(0.05) = 0.000125

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