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Chapter 4: Q5 (page 156)

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

LOL A U.S. Cellular survey of smartphone users showed that 26% of respondents answered 鈥測es鈥� when asked if abbreviations (such as LOL) are annoying when texting. What is the probability of randomly selecting a smartphone user and getting a response other than 鈥測es鈥�?

Short Answer

Expert verified

The probability of selecting a user who has answered other than 鈥測es鈥� is equal to 0.74.

Step by step solution

01

Given information

In a survey, 26% of the respondents answered 鈥測es鈥� to a question.

The question inquired, 鈥渋f abbreviations (such as LOL) are annoying when texting.鈥�

02

Define complementary events

If A stands for the occurrence of an event, then denotes the event that A does not occur. In that case, A and arecomplementary events.

Also,

PA+PA炉=1

03

Compute the probability of a complementary event

Let A be the event of selecting a user who answered 鈥測es鈥� to the question.

Then, A炉is the event of selecting a user who did not answer 鈥測es.鈥�

The percentages are divided by 100 to obtain the probability value.

It is calculated as shown below:

PA炉=1-PA=1-26100=74100=0.74

Therefore, the probability of selecting a respondent who answered other than 鈥測es鈥� is equal to 0.74.

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Most popular questions from this chapter

Surge Protectors Refer to the accompanying figure showing surge protectors p and q used to protect an expensive television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.985 probability of working correctly when a voltage surge occurs.

a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)

b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television? (Do not round the answer.)

c. Which arrangement should be used for better protection?

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炉?

In Exercises 5鈥�36, express all probabilities as fractions.

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

In Exercises 21鈥�24, use these results from the 鈥�1-Panel-THC鈥� test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana Use

a. How many subjects are included in the study?

b. How many of the subjects had a true negative result?

c. What is the probability that a randomly selected subject had a true negative result?

In Exercises 21鈥�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 got a result that is a false negative. Who would suffer from a false negative result? Why?
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