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Chapter 5: Q 1. (page 293)

Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to help determine whether a suspect is telling the truth. A lie detector test isn鈥檛 foolproof鈥攕ometimes it suggests that a person is lying when they鈥檙e actually telling the truth (a 鈥渇alse positive鈥�). Other times, the test says that the suspect is being truthful when the person is actually lying (a 鈥渇alse negative鈥�). For one brand of polygraph machine, the probability of a false positive is 0.08.
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative? Justify your answer.

Short Answer

Expert verified

Part (a) The truth is that people lie about 8% of the time, according to the machine.

Part (b) The truth is that people lie about 8% of the time, according to the machine.

Step by step solution

01

Part (a) Step 1. Given Information

A false positive has a 0.08 percent chance of occurring.

02

Part (a) Step 2. Concept Used

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between 0 (never happens) and 1 (happens frequently) (always occurs).

03

Part (a) Step 3. Calculation

The fraction of times an answer occurs is called a relative frequency, and it is calculated by dividing each frequency by the total number of students in the sample.

That is correct =0.08x100=8%

This probability is calculated as a long-run relative frequency by using a polygraph machine on a group of people who are all telling the truth. The machine will say that the people are lying around 8% of the time.

04

Part (b) Step 1. Explanation

The fraction of times an answer occurs is called a relative frequency, and it is calculated by dividing each frequency by the total number of students in the sample. Claiming someone is lying while they are stating the truth appears to be a more dangerous error than a false positive or false negative.

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Most popular questions from this chapter

Mac or PC? A recent census at a major university revealed that40% of its students primarily used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their

main computers. Suppose we select a student at random from among those who were part of the census.

(a) Assuming that there were 10,000 students in the census, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

(c) Consider the event that the randomly selected student is a graduate student who uses a Mac. Write this event in symbolic form using the two events of interest that you chose in (b).

(d) Find the probability of the event described in (c). Explain your method.

Twenty of a sample of 275 students say they are vegetarians. Of the vegetarians, 9eat both fish and eggs, 3 eat eggs but not fish, and 8 eat neither. Choose one of the vegetarians at random. What is the probability

that the chosen student eats neither fish nor eggs?

(a) 8/275=0.03 (c) 8/20=0.4 (e) 1

(b) 20/275=0.07 (d)

Tossing coins Refer to Exercise 40. Define event B: get more heads than tails. Find P(B).

Who eats breakfast? Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, 鈥淒o you eat breakfast on a regular basis?鈥� All 595 students in the school responded to the survey. The resulting data are shown in the two-way table

below.7 Male Female Total Eats breakfast regularly 190110300 Doesn鈥檛 eat breakfast regularly 130165295Total320275595

(a) Who are the individuals? What variables are being measured?

(b) If we select a student from the school at random, what is the probability that we choose

  • a female?
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regularly?

Blood types All human blood can be typed as one of O,A,B,or AB,but the distribution of the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American: Blood type: OABABProbability: 0.490.270.20?

(a) What is the probability of type AB blood? Why?

(b) What is the probability that the person chosen does not have type ABblood?

(c) Maria has type Bblood. She can safely receive blood transfusions from people with blood types Oand BWhat is the probability that a randomly chosen black American can donate blood to Maria?
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