/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q21 In Exercises 5鈥36, express all... [FREE SOLUTION] | 91影视

91影视

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

Phone Numbers Current rules for telephone area codes allow the use of digits 2鈥9 for the first digit, and 0鈥9 for the second and third digits. How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately preceding the last four digits of a phone number. Given both of those rules, how many 10-digit phone numbers are possible? Given that these rules apply to the United States and Canada and a few islands, are there enough possible phone numbers? (Assume that the combined population is about 400,000,000.)

Short Answer

Expert verified

The number of different area codes possible using the given rules is equal to 800.

The number of 10-digit phone numbers possible using the given rules is equal to 6,400,000,000.

Yes, there are enough possible phone numbers for the combined population of 400,000,000 people of the US and Canada.

Step by step solution

01

Given information

Different rules are applied to form 3-digit area codes and 10-digit phone numbers.

02

Counting principle

The number of different ways an event can occur is counted and multiplied using the given condition.

Here, two rules are provided for writing three digits:

Rule 1: The first digit is to be chosen from 2-9.

Rule 2: The second and third digits are to be chosen from 0-9.

03

Calculation

Area code (using rule 1 and rule 2):

The number of digits to choose from for the first digit of the area code = 8.

The number of digits to choose from for the second digit of the area code = 10.

The number of digits to choose from for the third digit of the area code = 10.

The total number of possible ways to write the area code:

81010=800

Therefore, the number of different area codes possible is equal to 800.

Phone number:

As the same two rules apply to the three digits of the phone number preceding the last four digits, the total number of ways to write those three digits is equal to 800.

The number of ways to write the first three digits = 800.

For the remaining four digits, the total number of digits to choose from (0-9) = 10.

The number of ways to write the remaining four digits:

10101010=10000

Thus, the total number of possible phone numbers is:

80080010000=6400000000

Therefore, the number of different phone numbers possible is equal to 6,400,000,000.

Since the combined population of the US and Canada has 400,000,000 people, while the possible number of phone numbers is greater,there are sufficient phone numbers available for both countries.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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?

Denomination Effect. In Exercises 13鈥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 鈥淭he Denomination Effect,鈥 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?

Redundancy. Exercises 25 and 26 involve redundancy.

Redundancy in Hospital Generators Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A hospital has two backup generators so that power is available if one of them fails during a power outage.

a. Find the probability that both generators fail during a power outage.

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?

Sobriety Checkpoint When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that PI= 0.00888, where I denotes the event of screening a driver and getting someone who is intoxicated. What doesPI denote, and what is its value?

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 If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.