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Chapter 4: Q12 (page 174)

In Exercises 5–36, express all probabilities as fractions.

Survey Reliability A survey with 12 questions is designed so that 3 of the questions are identical and 4 other questions are identical (except for minor changes in wording). How many different ways can the 12 questions be arranged?

Short Answer

Expert verified

The number of ways in which the 12 questions can be arranged is equal to 3326400.

Step by step solution

01

Given information

Out of 12 questions, three questions are alike, and four other questions are alike.

02

Permutation in case of identical units

When out of n units, someunits are identical to each other, the number of ways in which the n selected units (without replacement) can be arranged is given by the following formula:

n!n1!n2!....nk!

Here, n1units are identical, another set of n2units are identical, and so on until k.

03

Calculation

It is given that out of 12 questions, one set of four questions are alike, and another set of three questions are alike.

Here,

n=12k=2n1=3n2=4

The number of ways in which the 12 questions can be arranged is equal to the following:

n!n1!n2!....nk!=12!3!4!=3326400

Therefore, the number of ways in which the 12 questions can be arranged is equal to 3326400.

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Most popular questions from this chapter

Exclusive Or The exclusive or means either one or the other events occurs, but not both.

a. For the formal addition rule, rewrite the formula for P(A or B) assuming that the addition rule uses the exclusive or instead of the inclusive or.

b. Repeat Exercise 11 “Fast Food Drive-Thru Accuracy” using the exclusive or instead of the inclusive or.

At Least One. In Exercises 5–12, find the probability.

At Least One Defective iPhone It has been reported that 20% of iPhones manufactured by Foxconn for a product launch did not meet Apple’s quality standards. An engineer needs at least one defective iPhone so she can try to identify the problem(s). If she randomly selects 15 iPhones from a very large batch, what is the probability that she will get at least 1 that is defective? Is that probability high enough so that she can be reasonably sure of getting a defect for her work?

New Jersey Lottery Let A denote the event of placing a $1 straight bet on the New Jersey Pick 3 lottery and winning. There are 1000 different ways that you can select the three digits (with repetition allowed) in this lottery, and only one of those three-digit numbers will be the winner. What is the value of? What is the value ofPA¯?

In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

McDonald’s

Burger King

Wendy’s

Taco Bell

Order Accurate

329

264

249

145

OrderNotAccurate

33

54

31

13

Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that both of them are not accurate.

a. Assume that the selections are made with replacement. Are the events independent?

b. Assume that the selections are made without replacement. Are the events independent?

Probability of At Least One Let A = the event of getting at least 1 defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If 5% of the iPhones in a batch are defective and the other 95% are all good, which of the following are correct?

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
See all solutions

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