Elementary Statistics: A Step-by-Step Approach with Formula Card
Elementary Statistics: A Step-by-Step Approach with Formula Card
9th Edition
ISBN: 9780078136337
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
Question
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Chapter 4.3, Problem 34E

a.

To determine

To obtain: Theprobability that the adoption was from Ethiopia given that it was from 2010.

a.

Expert Solution
Check Mark

Answer to Problem 34E

The probabilitythat the adoption was from Ethiopia given that it was from 2010 is 0.359.

Explanation of Solution

Given info:

The data shows that the numbers offoreign adoptions from the United States.

Calculation:

The total number of adoptions is shown in the Table (1).

  2006 2010 Total
China 6,493 3,401 9,894
Ethiopia 732 2,513 3,245
Russia 3,706 1,082 4,788
Total 10,931 6,996 17,927

Table (1)

Let event A denote that theadoptionwas from 2010 and event B denote thatthe adoption was from Ethiopia.

The formula for probability of event A is,

P(A)=Number of outcomes in ATotal number of outcomes in the sample space

Substitute ‘6,996’ for ‘Number of outcomes in A’ and 17,927 for ‘Total number of outcomes in the sample space’,

P(A)=6,99617,927=0.39

The formula for probability of event A and B is,

P(A and B)=Number of outcomes in A and BTotal number of outcomes in the sample space

Substitute ‘2,513’for ‘Number of outcomes in A and B’ and 17,927 for ‘Total number of outcomes in the sample space’,

P(A and B)=2,51317,927=0.14

Conditional rule:

The formula for probability of A given B is, P(B|A)=P(A and B)P(A)

Substitute 0.14 for ‘ P(A and B) ’ and 0.39for P(A) .

The required probability is,

P(B|A)=P(A and B)P(A)=0.140.39=0.359

Thus, the probability that the adoption was from Ethiopia given that it was from 2010 is 0.359.

b.

To determine

To obtain: The probability that the adoptionwas from Russia and in 2006.

b.

Expert Solution
Check Mark

Answer to Problem 34E

The probability that the adoptionwas from Russia and in 2006is 0.074.

Explanation of Solution

Let event C denote that the adoption was from Russia and event D denote that adoption was in 2006.

The formula for probability of event C and D is,

P(C and D)=Number of outcomes in C and DTotal number of outcomes in the sample space

Substitute 3,706 for ‘Number of outcomes in C and D’ and 17,927 for ‘Total number of outcomes in the sample space’,

P(C and D)=3,70617,927=0.207

Thus, the probability that the adoptionwas from Russiaand in 2006 is 0.207.

c.

To determine

To obtain: The probability that the adoptiondid not occur in 2006 and was not from Ethiopia.

c.

Expert Solution
Check Mark

Answer to Problem 34E

The probability that the adoption did not occur in 2006 and was not from Ethiopiais 0.25.

Explanation of Solution

Let event E denote that theadoptionwas from Ethiopiaand event D denote thatadoptionwas from 2006.

The formula for probability of event E¯ and D¯ is,

P(E¯ and D¯)=Number of outcomes in E¯ and D¯Total number of outcomes in the sample space

Substitute ‘4,483 =(3,401+1,082) for ‘Number of outcomes in E¯ and D¯ ’ and 17,927 for ‘Total number of outcomes in the sample space’,

P(E¯ and D¯)=4,48317,927=0.25

Thus, the probability that the adoptionwas did not occur in 2006 and was not from Ethiopiais 0.25.

d.

To determine

To obtain: The probabilitythatboth the adoptionsare from china.

d.

Expert Solution
Check Mark

Answer to Problem 34E

The probabilitythat both the adoptionsare from china is

Explanation of Solution

Given info:

There are 2 adoptionschosen at random.

Calculation:

Multiplicationrule:

If the A and B are independent, then P(A and B)=P(A)P(B) .

Let event F denote that theadoptionwas from china.

The formula for probability of event F is,

P(F)=Number of outcomes in FTotal number of outcomes in the sample space

Substitute 9,894 for ‘Number of outcomes in F’ and 17,927 for ‘Total number of outcomes in the sample space’,

P(F)=9,89417,927=0.552

Hence, the probabilitythat theadoptionwas from chinais 0.552.

Each adoption is independent of the other.

By applying multiplication rule, the required probability is,

P(F and F)=P(F)×P(F)=0.552×0.552=0.305

Therefore, the probabilitythat both the adoptionsare from china is 0.305.

Interpretation:

There is a 0.305 probabilitythat both the adoptionsare from china.

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Chapter 4 Solutions

Elementary Statistics: A Step-by-Step Approach with Formula Card

Ch. 4.1 - A probability experiment is conducted. Which of...Ch. 4.1 - Classify each statement as an example of classical...Ch. 4.1 - Classify each statement as an example of classical...Ch. 4.1 - Prob. 13ECh. 4.1 - Rolling a Die If a die is rolled one time, find...Ch. 4.1 - Prob. 15ECh. 4.1 - Rolling Two Dice If two dice are rolled one time,...Ch. 4.1 - Prob. 17ECh. 4.1 - Drawing a Card If a card is drawn from a deck,...Ch. 4.1 - Shopping Mall Promotion A shopping mall has set up...Ch. 4.1 - Selecting a State Choose one of the 50 states at...Ch. 4.1 - Human Blood Types Human blood is grouped into four...Ch. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Rural Speed Limits Rural speed limits for all 50...Ch. 4.1 - Prob. 25ECh. 4.1 - Sources of Energy Uses in the United States A...Ch. 4.1 - Prob. 27ECh. 4.1 - Computers in Elementary Schools Elementary and...Ch. 4.1 - College Debt The following information shows the...Ch. 4.1 - Population of Hawaii The population of Hawaii is...Ch. 4.1 - Prob. 31ECh. 4.1 - Living Arrangements for Children Here are the...Ch. 4.1 - Prob. 33ECh. 4.1 - Federal Government Revenue The source of federal...Ch. 4.1 - Selecting a Bill A box contains a 1 bill, a 5...Ch. 4.1 - Tossing Coins Draw a tree diagram and determine...Ch. 4.1 - Prob. 37ECh. 4.1 - Family Dinner Combinations A family special at a...Ch. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Distribution of CEO Ages The distribution of ages...Ch. 4.1 - Tossing a Coin A person flipped a coin 100 times...Ch. 4.1 - Medical Treatment A medical doctor stated that...Ch. 4.1 - Wheel Spinner The wheel spinner shown here is spun...Ch. 4.1 - Tossing Coins Toss three coins 128 times and...Ch. 4.1 - Applying the Concepts 41 Tossing a Coin Assume you...Ch. 4.1 - Odds Odds are used in gambling games to make them...Ch. 4.2 - Applying the Concepts 42 Which Pain Reliever Is...Ch. 4.2 - Define mutually exclusive events, and give an...Ch. 4.2 - Explain briefly why addition rule 2 can be used...Ch. 4.2 - Prob. 3ECh. 4.2 - Determine whether these events are mutually...Ch. 4.2 - College Degrees Awarded The table below represents...Ch. 4.2 - Riding to School The probability that John will...Ch. 4.2 - Medical Specialities The following doctors were...Ch. 4.2 - U.S. Population The data show the U.S. population...Ch. 4.2 - Prob. 9ECh. 4.2 - Selecting a Movie A media rental store rented the...Ch. 4.2 - Prob. 11ECh. 4.2 - Selecting a Book At a used-book sale, 100 books...Ch. 4.2 - Young Adult Residences According to the Bureau of...Ch. 4.2 - Endangered Species The chart below shows the...Ch. 4.2 - Multiple Births The number of multiple births in...Ch. 4.2 - Licensed Drivers in the United States In a recent...Ch. 4.2 - Prob. 17ECh. 4.2 - Mail Delivery A local postal carrier distributes...Ch. 4.2 - Medical Tests on Emergency Patients The frequency...Ch. 4.2 - College Fundraiser A social organization of 32...Ch. 4.2 - Prob. 21ECh. 4.2 - Medical Patients A recent study of 300 patients...Ch. 4.2 - Prob. 23ECh. 4.2 - Rolling Die Two dice are rolled. Find the...Ch. 4.2 - Prob. 25ECh. 4.2 - Rolling Dice Three dice are rolled. Find the...Ch. 4.2 - Prob. 27ECCh. 4.2 - Building a New Home In building new homes, a...Ch. 4.2 - Prob. 29ECCh. 4.2 - Prob. 30ECCh. 4.2 - Prob. 31ECCh. 4.2 - Events A and B are mutually exclusive with P(A)...Ch. 4.3 - Prob. 1ACCh. 4.3 - State which events are independent and which are...Ch. 4.3 - State which events are independent and which are...Ch. 4.3 - Video and Computer Games Sixty-nine percent of...Ch. 4.3 - Seat Belt Use The Gallup Poll reported that 52% of...Ch. 4.3 - Automobile Sales An automobile salesperson finds...Ch. 4.3 - Prison Populations If 25% of U.S. federal prison...Ch. 4.3 - Prob. 7ECh. 4.3 - Working Women and Computer Use It is reported that...Ch. 4.3 - Prob. 9ECh. 4.3 - Selecting Marbles A bag contains 9 red marbles, 8...Ch. 4.3 - Prob. 11ECh. 4.3 - Flashlight Batteries A flashlight has 6 batteries,...Ch. 4.3 - Prob. 13ECh. 4.3 - Scientific Study In a scientific study there are 8...Ch. 4.3 - Prob. 15ECh. 4.3 - Winning a Door Prize At a gathering consisting of...Ch. 4.3 - Prob. 17ECh. 4.3 - Sales A manufacturer makes two models of an item:...Ch. 4.3 - Student Financial Aid In a recent year 8,073,000...Ch. 4.3 - Selecting Colored Balls Urn 1 contains 5 red balls...Ch. 4.3 - Automobile Insurance An insurance company...Ch. 4.3 - Defective Items A production process produces an...Ch. 4.3 - Prison Populations For a recent year, 0.99 of the...Ch. 4.3 - Rolling Dice Roll two standard dice and add the...Ch. 4.3 - Heart Disease Twenty-five percent of all deaths...Ch. 4.3 - Country Club Activities At the Avonlea Country...Ch. 4.3 - College Courses At a large university, the...Ch. 4.3 - Congressional Terms Below is given the summary...Ch. 4.3 - Pizza and Salads In a pizza restaurant, 95% of the...Ch. 4.3 - Gift Baskets The Gift Basket Store had the...Ch. 4.3 - Blood Types and Rh Factors In addition to being...Ch. 4.3 - Doctor Specialties Below are listed the numbers of...Ch. 4.3 - Lightning Strikes It has been said that the...Ch. 4.3 - Prob. 34ECh. 4.3 - Leisure Time Exercise Only 27% of U.S. adults get...Ch. 4.3 - Customer Purchases In a department store there are...Ch. 4.3 - Marital Status of Women According to the...Ch. 4.3 - Fatal Accidents The American Automobile...Ch. 4.3 - On-Time Airplane Arrivals According to FlightStats...Ch. 4.3 - On-Time Flights A flight from Pittsburgh to...Ch. 4.3 - Reading to Children Fifty-eight percent of...Ch. 4.3 - Doctoral Assistantships Of Ph.D. students, 60%...Ch. 4.3 - Prob. 43ECh. 4.3 - Autism In recent years it was thought that...Ch. 4.3 - Prob. 45ECh. 4.3 - Medication Effectiveness A medication is 75%...Ch. 4.3 - Prob. 47ECh. 4.3 - Selecting a Letter of the Alphabet If 3 letters of...Ch. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Selecting a Flower In a large vase, there are 8...Ch. 4.3 - Let A and B be two mutually exclusive events. Are...Ch. 4.3 - Types of Vehicles The Bargain Auto Mall has the...Ch. 4.3 - Prob. 55ECCh. 4.3 - Commercials Event A is the event that a person...Ch. 4.3 - Given a sample space with events A and B such that...Ch. 4.3 - Childs Board Game In a childs board game of the...Ch. 4.3 - Bags Containing Marbles Two bags contain marbles....Ch. 4.4 - Garage Door Openers Garage door openers originally...Ch. 4.4 - Zip Codes How many 5-digit zip codes are possible...Ch. 4.4 - Letter Permutations List all the permutations of...Ch. 4.4 - Prob. 3ECh. 4.4 - Visiting Nurses How many different ways can a...Ch. 4.4 - Quinto Lottery A lottery game called Quinto is...Ch. 4.4 - Show Programs Three bands and two comics are...Ch. 4.4 - Prob. 7ECh. 4.4 - Radio Station Call Letters The call letters of a...Ch. 4.4 - Prob. 9ECh. 4.4 - Secret Code Word How many 4-letter code words can...Ch. 4.4 - Passwords Given the characters A, B, C, H, I, T,...Ch. 4.4 - Automobile Trips There are 2 major roads from city...Ch. 4.4 - Prob. 13ECh. 4.4 - Evaluate each expression. a. 6! b. 11! c. 2! d. 9!...Ch. 4.4 - Sports Car Stripes How many different 4-color code...Ch. 4.4 - Manufacturing Tests An inspector must select 3...Ch. 4.4 - Prob. 17ECh. 4.4 - Inspecting Restaurants How many different ways can...Ch. 4.4 - Prob. 19ECh. 4.4 - Word Permutation How many different 4-letter...Ch. 4.4 - ID Cards How many different ID cards can be made...Ch. 4.4 - Free-Sample Requests An online coupon service has...Ch. 4.4 - Ticket Selection How many different ways can 4...Ch. 4.4 - Movie Selections The Foreign Language Club is...Ch. 4.4 - Task Assignments How many ways can an adviser...Ch. 4.4 - Agency Cases An investigative agency has 7 cases...Ch. 4.4 - Signal Flags How many different flag signals, each...Ch. 4.4 - Word Permutations How many permutations can be...Ch. 4.4 - Code Words How many different 9-letter code words...Ch. 4.4 - Toothpaste Display How many different ways can 5...Ch. 4.4 - Book Arrangements How many different ways can 6...Ch. 4.4 - Word Permutations How many permutations can be...Ch. 4.4 - Evaluate each expression. a. 5C2 b. 8C3 c. 7C4 d....Ch. 4.4 - Evaluate each expression. a. 3C0 b. 3C3 c. 9C7 d....Ch. 4.4 - Prob. 35ECh. 4.4 - Selecting Players How many ways can 4 baseball...Ch. 4.4 - Prob. 37ECh. 4.4 - Selecting Christmas Presents If a person can...Ch. 4.4 - Buffet Desserts In how many ways can you choose 3...Ch. 4.4 - Bridge Foursomes How many different tables of 4...Ch. 4.4 - Music Recital Six students are performing one song...Ch. 4.4 - Freight Train Cars In a train yard there are 4...Ch. 4.4 - Selecting a Committee There are 7 women and 5 men...Ch. 4.4 - Buffet Desserts In how many ways can you choose 3...Ch. 4.4 - Hawaiian Words The Hawaiian alphabet consists of 7...Ch. 4.4 - Selecting a Jury How many ways can a jury of 6...Ch. 4.4 - Selecting Students How many ways can you pick 4...Ch. 4.4 - Investigative Team The state narcotics bureau must...Ch. 4.4 - Prob. 49ECh. 4.4 - Charity Event Participants There are 16 seniors...Ch. 4.4 - Prob. 51ECh. 4.4 - DVD Selection How many ways can a person select 8...Ch. 4.4 - Prob. 53ECh. 4.4 - Selecting a Location An advertising manager...Ch. 4.4 - Prob. 55ECh. 4.4 - Test Marketing Products Anderson Research Company...Ch. 4.4 - Prob. 57ECh. 4.4 - Selecting Musicals How many different ways can a...Ch. 4.4 - Textbook Selection How many different ways can an...Ch. 4.4 - DVD Selection How many ways can a person select 8...Ch. 4.4 - Prob. 61ECh. 4.4 - Signal Flags How many different signals can be...Ch. 4.4 - Prob. 63ECh. 4.4 - Air Pollution The Environmental Protection Agency...Ch. 4.4 - Selecting Officers In a board of directors...Ch. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECCh. 4.4 - Prob. 68ECCh. 4.4 - Seating in a Movie Theater How many different ways...Ch. 4.4 - Prob. 70ECCh. 4.4 - Prob. 71ECCh. 4.4 - Prob. 72ECCh. 4.5 - Applying the Concepts 45 Counting Rules and...Ch. 4.5 - Selecting Cards Find the probability of getting 2...Ch. 4.5 - Selecting Cards Cards numbered 110 are shuffled...Ch. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Job Applications Six men and seven women apply for...Ch. 4.5 - Defective Resistors A package contains 12...Ch. 4.5 - Prob. 7ECh. 4.5 - Getting a Full House Find the probability of...Ch. 4.5 - World-Class Orchestras About.coms list of 20 World...Ch. 4.5 - Selecting Cards The red face cards and the black...Ch. 4.5 - Socks in a Drawer A drawer contains 11 identical...Ch. 4.5 - Selecting Books Find the probability of selecting...Ch. 4.5 - Prob. 13ECh. 4.5 - Football Team Selection A football team consists...Ch. 4.5 - Arrangement of Washers Find the probability that...Ch. 4.5 - Poker Hands Using the information in Exercise 70...Ch. 4.5 - Prob. 17ECh. 4 - Prob. 4.1.1RECh. 4 - Selecting a Card When a card is selected from a...Ch. 4 - Software Selection The top-10 selling computer...Ch. 4 - Motor Vehicle Producers The top five motor vehicle...Ch. 4 - Prob. 4.1.5RECh. 4 - Rolling Two Dice When two dice are rolled, find...Ch. 4 - Prob. 4.2.7RECh. 4 - Breakfast Drink In a recent survey, 18 people...Ch. 4 - Prob. 4.2.9RECh. 4 - Prob. 4.2.10RECh. 4 - Online Course Selection Roughly 1 in 6 students...Ch. 4 - Purchasing Sweaters During a sale at a mens store,...Ch. 4 - Drawing Cards Three cards are drawn from an...Ch. 4 - Coin Toss and Card Drawn A coin is tossed and a...Ch. 4 - Movie Releases The top five countries for movie...Ch. 4 - Factory Output A manufacturing company has three...Ch. 4 - Effectiveness of Vaccine A vaccine has a 90%...Ch. 4 - T-shirt Factories Two T-shirt printing factories...Ch. 4 - Car Purchase The probability that Sue will live on...Ch. 4 - Prob. 4.3.20RECh. 4 - Prob. 4.3.21RECh. 4 - Bad Weather The probability that it snows and the...Ch. 4 - Education Level and Smoking At a large factory,...Ch. 4 - Prob. 4.3.24RECh. 4 - Prob. 4.3.25RECh. 4 - Prob. 4.3.26RECh. 4 - Prob. 4.4.27RECh. 4 - Prob. 4.4.28RECh. 4 - Prob. 4.4.29RECh. 4 - Prob. 4.4.30RECh. 4 - Prob. 4.4.31RECh. 4 - Committee Representation There are 6 Republican, 5...Ch. 4 - Song Selections A promotional MP3 player is...Ch. 4 - Prob. 4.4.34RECh. 4 - Prob. 4.4.35RECh. 4 - Prob. 4.4.36RECh. 4 - Prob. 4.4.37RECh. 4 - Prob. 4.4.38RECh. 4 - Prob. 4.4.39RECh. 4 - Prob. 4.4.40RECh. 4 - Prob. 4.5.41RECh. 4 - License Plates A certain states license plate has...Ch. 4 - Territorial Selection Several territories and...Ch. 4 - Yahtzee Yahtzee is a game played with 5 dice....Ch. 4 - Personnel Classification For a survey, a subject...Ch. 4 - Determine whether each statement is true or false....Ch. 4 - Determine whether each statement is true or false....Ch. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Determine whether each statement is true or false....Ch. 4 - Determine whether each statement is true or false....Ch. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - When a meteorologist says that there is a 30%...Ch. 4 - The sample space for tossing 3 coins consists of...Ch. 4 - Prob. 12CQCh. 4 - When two dice are rolled, the sample space...Ch. 4 - Prob. 14CQCh. 4 - What is the number of permutations of 6 different...Ch. 4 - Prob. 16CQCh. 4 - Prob. 17CQCh. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Complete the following statements with the best...Ch. 4 - Prob. 23CQCh. 4 - Selecting a Card When a card is drawn from a deck,...Ch. 4 - Selecting a Sweater At a mens clothing store, 12...Ch. 4 - Prob. 26CQCh. 4 - Appliance Ownership The probability that a person...Ch. 4 - Starting Salaries Of the physics graduates of a...Ch. 4 - Prob. 29CQCh. 4 - Scholarships The probability that Samantha will be...Ch. 4 - Prob. 31CQCh. 4 - Prob. 32CQCh. 4 - Work and Weather The probability that Mike has to...Ch. 4 - Education of Factory Employees At a large factory,...Ch. 4 - Heart Attacks In a certain high-risk group, the...Ch. 4 - Rolling a Die A single die is rolled 4 times. Find...Ch. 4 - Prob. 37CQCh. 4 - Singer Selection How many ways can 5 sopranos and...Ch. 4 - Speaker Selection How many different ways can 8...Ch. 4 - Stocking Machines A soda machine servicer must...Ch. 4 - ID Cards One companys ID cards consist of 5...Ch. 4 - Prob. 42CQCh. 4 - Prob. 43CQCh. 4 - Prob. 44CQCh. 4 - Prob. 45CQCh. 4 - Cruise Ship Activities A cruise director schedules...Ch. 4 - Prob. 47CQCh. 4 - Prob. 48CQCh. 4 - Toy Display A toy store manager wants to display 7...Ch. 4 - Commercial Order A local television station must...Ch. 4 - Prob. 1CTCCh. 4 - Prob. 2CTCCh. 4 - Prob. 3CTCCh. 4 - Prob. 4CTCCh. 4 - Prob. 4DP
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