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Chapter 4: Q14 (page 174)

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

Electricity When testing for current in a cable with five color-coded wires, the author used a meter to test two wires at a time. How many different tests are required for every possible pairing of two wires?

Short Answer

Expert verified

The number of tests required for testing every possible pair is equal to 10.

Step by step solution

01

Given information

There are five color-coded wires. Two wires are paired each time to test the current in a cable.

02

Define combination

The combination is used to determine the total ways of choosing r items out of the nitemswithout replacing the order of the items and considering the order of the items.

Mathematically, the formula of combination is as follows:

Crn=n!n-r!r!

03

Calculation

The number of different wires is five.

The total number of ways in which a pair of wires from five different wires can be selected without replacement is computed as shown below:

5C2=5!5-2!2!=10

Therefore, the number of tests required for each pair is equal to 10.

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Most popular questions from this chapter

Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using a \(1 bill or a \)1 bill, college students were given either a \(1 bill or a \)1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Purchased Gum

Kept the Money

Students Given A \(1 bill

27

46

Students Given a \)1 bill

12

34

Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.

c. What do the preceding results suggest?

In Exercises 29 and 30, find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used.

Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma,” by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15).

a. If 1 of the 159,511 patients in the study is randomly selected, what is the probability that the subject was transported by helicopter?

b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter

Acceptance Sampling. With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is found to be okay. Exercises 27 and 28 involve acceptance sampling.

Something Fishy: The National Oceanic and Atmospheric Administration (NOAA) inspects seafood that is to be consumed. The inspection process involves selecting seafood samples from a larger “lot.” Assume a lot contains 2875 seafood containers and 288 of these containers include seafood that does not meet inspection requirements. What is the probability that 3 selected container samples all meet requirements and the entire lot is accepted based on this sample? Does this probability seem adequate?

In Exercises 21–24, refer to the sample data in Table 4-1, which is included with the Chapter Problem. Assume that 1 of the 555 subjects included in Table 4-1 is randomly selected.


Positive Test Result

(Test shows drug use)

Negative Test Result

(Test shows no drug use)

Subject Uses Drugs

45 (True Positive)

5 (False Negative)

Subject Does Not Use drugs

25 (False Positive)

480 (True Negative)

Drug Testing Job Applicants Find the probability of selecting someone who uses drugs. Does the result appear to be reasonable as an estimate of the “prevalence rate” described in the Chapter Problem?

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

SAT Test When making a random guess for an answer to a multiple-choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.
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