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Chapter 4: Q17 (page 143)

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

Randomness When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero

Short Answer

Expert verified

The probability that the digit of a phone number is chosen to be 0 is 0.1.

Step by step solution

01

Given information

The last digit of a phone number is randomly generated from 0 to 9.

02

Define probability

Probability is the measure of how likely an event is to happen.

Its formula is

PA=NumberofoutcomesinfavourofATotalnumberofoutcomes

The value of probability lies between 0 and 1 (inclusive).

03

Calculate the probability 

There is a 1 in 10 chance that the last digit is 0. It meansthere is one favorable digit (0) for the event from 10 choices (0 through 9).

The total number of digits from 0 to 9 is 10.

The number of zeros in this range is 1.

The probability of getting a zero is

PGettingazero=110=0.1

Therefore, the probability of getting a zero in the random generation of digits is 0.1.

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Most popular questions from this chapter

In Exercises 25–32, find the probability and answer the questions.. Car Rollovers In a recent year in the United States, 83,600 passenger cars rolled over when they crashed, and 5,127,400 passenger cars did not roll over when they crashed. Find the probability that a randomly selected passenger car crash results in a rollover. Is it unlikely for a car to roll over in a crash?

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 they are both 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?

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?

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?

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.
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