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mathematics
statistics
Fundamentals Of Statistics 4th Edition Michael Sullivan III - Solutions
The following data represent the number of speeding tickets issued to individuals in the past year and the gender of the individuals. Determine the following probabilities based on the results of the survey.(a) What is the probability that a randomly selected individual was issued no tickets last
The following data represent the number of trafï¬c fatalities in the United States in 2009 by seat location and gender.(a) Among female fatalities, what is the probability that a randomly selected fatality is the driver? (b) Among passenger fatalities, what is the probability that a
The following data represent the number of drivers involved in fatal crashes in the United States in 2009 by day of the week and gender.(a) Among Sunday fatal crashes, what is the probability that a randomly selected fatality is female? (b) Among female fatalities, what is the probability that a
Suppose that you just received a shipment of six televisions. Two of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability that at least one does not work?
A committee consists of four women and three men. The committee will randomly select two people to attend a conference in Hawaii. Find the probability that both are women.
Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is a king and the second card is a king if the sampling is done without replacement? (b) What is the probability that the first card is a king and the second card is a king
Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is a club and the second card is a club if the sampling is done without replacement? (b) What is the probability that the first card is a club and the second card is a club
This past semester, I had a small business calculus section. The students in the class were Mike, Neta, Jinita, Kristin, and Dave. Suppose that I randomly select two people to go to the board to work problems. What is the probability that Dave is the first person chosen to go to the board and Neta
My wife has organized a monthly neighborhood party. Five people are involved in the group: Yolanda (my wife), Lorrie, Laura, Kim, and Anne Marie. They decide to randomly select the first and second home that will host the party. What is the probability that my wife hosts the first party and
Suppose that a compact disc (CD) you just purchased has 13 tracks. After listening to the CD, you decide that you like 5 of the songs. With the random feature on your CD player, each of the 13 songs is played once in random order. Find the probability that among the first two songs played (a) You
Due to a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12-pack. Suppose that two cans are randomly selected from the 12-pack. (a) Determine the probability that both contain diet soda. (b) Determine the probability that both contain
A bag of 30 tulip bulbs purchased from a nursery contains 12 red tulip bulbs, 10 yellow tulip bulbs, and 8 purple tulip bulbs. Use a tree diagram like the one in Example 5 to answer the following: (a) What is the probability that two randomly selected tulip bulbs are both red? (b) What is the
The local golf store sells an “onion bag” that contains 35 “experienced” golf balls. Suppose that the bag contains 20 Titleists, 8 Maxflis, and 7 Top-Flites. Use a tree diagram like the one in Example 5 to answer the following: (a) What is the probability that two randomly selected golf
According to the National Center for Health Statistics, there is a 20.3% probability that a randomly selected resident of the United States aged 18 years or older is a smoker. In addition, there is a 44.5% probability that a randomly selected resident of the United States aged 18 years or older is
According to the U.S. Bureau of Labor Statistics, there is a 4.9% probability that a randomly selected employed individual has more than one job (a multiple-job holder). Also, there is a 46.6% probability that a randomly selected employed individual is male, given that he has more than one job.
Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: (a) Compute the probability that 10 people have 10 different birthdays. (b) The complement of
Using the procedure given in Problem 33, compute the probability that at least 2 people in a room of 23 people share the same birthday.
The following data represent the number of different communication activities (e.g., cell phone, text messaging, e-mail, Internet, and so on) used by a random sample of teenagers over the past 24 hours.(a) Are the events €œmale€ and €œ0 activities€
The following data represent political party by age from a random sample of registered Iowa Voters.(a) Are the events €œRepublican€ and €œ30-44€ independent? Justify your answer. (b) Are the events €œDemocrat€ and
A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Answer the following questions to obtain the probability of being dealt a flush in five cards. (a) We initially concentrate on one suit, say clubs. There are 13
A royal flush in the game of poker occurs if the player gets the cards Ten, Jack, Queen, King, and Ace all in the same suit. Use the procedure given in Problem 37 to compute the probability of being dealt a royal flush.
Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000
Suppose that a poll is being conducted in the village of Lemont. The pollster identifies her target population as all residents of Lemont 18 years old or older. This population has 6494 people. (a) Compute the probability that the first resident selected to participate in the poll is Roger
Refer to the contingency table in Problem 17 that relates age and likelihood to buy American. Determine P(45-54 years old) and P(45-54 years old|more likely). Are the events €œ45-54 years old€ and €œmore likely€ independent?
Refer to the contingency table in Problem 18 that relates number of speeding tickets and gender. Determine P(female) and P(female|1 ticket). Are the events €œ1 ticket€ and €œfemale€independent?
Refer to the contingency table in Problem 19 that relates person type in a trafï¬c fatality to gender. Determine P(female) and P(female|driver). Are the events €œfemale€ and €œdriver€ independent?
Refer to the contingency table in Problem 20 that relates gender to day of the week. Determine P(male) and P(male|Wednesday). Are the events €œmale€ and €œWednesday€ independent?
Let’s Make a Deal In 1991, columnist Marilyn Vos Savant posted her reply to a reader’s question. The question posed was in reference to one of the games played on the gameshow Let’s Make a Deal hosted by Monty Hall.Suppose you’re on a game show, and you’re given
Find the value of permutation. 6P2
Find the value of permutation. 7P2
Find the value of permutation. 4P4
Find the value of permutation. 7P7
Find the value of permutation. 5P0
Find the value of permutation. 4P0
Find the value of permutation. 8P3
Find the value of permutation. 9P4
Find the value of combination. 8C3
Find the value of combination. 9C2
Find the value of combination. 10C2
Find the value of combination. 12C3
Find the value of combination. 52C1
Find the value of combination. 40C40
Find the value of combination. 48C3
Find the value of combination. 30C4
Suppose Dan is going to burn a compact disc (CD) that will contain 12 songs. In how many ways can Dan arrange the 12 songs on the CD?
Arranging Students In how many ways can 15 students be lined up?
A salesperson must travel to eight cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?
A certain compact disc player randomly plays each of 10 songs on a CD. Once a song is played, it is not repeated until all the songs on the CD have been played. In how many different ways can the CD player play the 10 songs?
Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by either one, two, or three letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the New York Stock Exchange?
Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either four or five letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NASDAQ?
Outside a home there is a keypad that will open the garage if the correct four-digit code is entered. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn’t remember the code?
A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx–xx–xxxx, where each x is a digit from 0 to 9. (a) How many Social Security numbers can be formed? (b) What is the probability of correctly guessing the Social Security number
How many user names are possible in Problem 41 if the last character must be a digit?
A combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed. (a) How many different lock combinations are there? (b) What is the probability of guessing a
How many different license plate numbers can be made by using one letter followed by five digits selected from the digits 0 through 9?
Suppose 40 cars start at the Indianapolis 500. In how many ways can the top 3 cars finish the race?
In how many ways can the top 2 horses finish in a 10-horse race?
Four members from a 20-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different
Four members from a 50-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different
A lottery exists where balls numbered 1 to 25 are placed in an urn. To win, you must match the four balls chosen in the correct order. How many possible outcomes are there for this game?
In the U.S. Senate, there are 21 members on the Committee on Banking, Housing, and Urban Affairs. Nine of these 21 members are selected to be on the Subcommittee on Economic Policy. How many different committee structures are possible for this subcommittee?
How many different simple random samples of size 5 can be obtained from a population whose size is 50?
How many different simple random samples of size 7 can be obtained from a population whose size is 100?
A family has six children. If this family has exactly two boys, how many different birth and gender orders are possible?
A family has eight children. If this family has exactly three boys, how many different birth and gender orders are possible?
In the Illinois Lottery game Little Lotto, an urn contains balls numbered 1 to 39. From this urn, 5 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of five numbers. To win, all five numbers must match those chosen from the urn. The order in which the balls
In Mega Millions, an urn contains balls numbered 1 to 56, and a second urn contains balls numbered 1 to 46. From the first urn, 5 balls are chosen randomly, without replacement and without regard to order. From the second urn, 1 ball is chosen randomly. For a $1 bet, a player chooses one set of
The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c)
Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly. (a) What is the probability that the committee is composed of all Democrats? (b) What is the probability that the committee is
Suppose that a shipment of 120 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality-control engineer randomly selects 4 of the components and tests them. If 1 or more of the components is defective, the shipment is rejected. What is
A box containing twelve 40-watt light bulbs and eighteen 60-watt light bulbs is stored in your basement. Unfortunately, the box is stored in the dark and you need two 60-watt bulbs. What is the probability of randomly selecting two 60-watt bulbs from the box?
Suppose a compact disc (CD) you just purchased has 13 tracks. After listening to the CD, you decide that you like 5 of the songs. The random feature on your CD player will play each of the 13 songs once in a random order. Find the probability that among the first 4 songs played (a) you like 2 of
Through a manufacturing error, three cans marked “regular soda” were accidentally filled with diet soda and placed into a 12-pack. Suppose that three cans are randomly selected from the 12-pack. (a) Determine the probability that exactly two contain diet soda. (b) Determine the probability
You are dealt 5 cards from a standard 52-card deck. Determine the probability of being dealt three of a kind (such as three aces or three kings) by answering the following questions: (a) How many ways can 5 cards be selected from a 52-card deck? (b) Each deck contains 4 twos, 4 threes, and so on.
You are dealt 5 cards from a standard 52-card deck. Determine the probability of being dealt two of a kind by answering the following questions: (a) How many ways can 5 cards be selected from a 52-card deck? (b) Each deck contains 4 twos, 4 threes, and so on. How many ways can three of the same
Suppose that you have just received a shipment of 20 modems. Although you don’t know this, 3 of the modems are defective. To determine whether you will accept the shipment, you randomly select 4 modems and test them. If all 4 modems work, you accept the shipment. Otherwise, the shipment is
Suppose that you have just received a shipment of 100 televisions. Although you don’t know this, 6 are defective. To determine whether you will accept the shipment, you randomly select 5 televisions and test them. If all 5 televisions work, you accept the shipment; otherwise, the shipment is
According to the Sefton Council Password Policy (August 2007), the United Kingdom government recommends the use of “Environ passwords with the following format: consonant, vowel, consonant, consonant, vowel, consonant, number, number (for example, pinray45).” (a) Assuming passwords are not case
List all permutations of five objects a, b, c, d, and e taken three at a time without replacement.
Find P(E or F ) if E and F are mutually exclusive. Find the probability of the indicated event if P(E) = 0.7 and P(F ) = 0.2.
Find P(E or F ) if P(E and F ) = 0.15. Find the probability of the indicated event if P(E) = 0.7 and P(F ) = 0.2.
Evaluate expression. 7P3
Evaluate expression. 9C4
Suppose that events E and F are independent, P(E) = 0.8, and P(F ) = 0.5. What is P(E and F )?
Suppose that E and F are two events and P(E and F ) = 0.4 and P(E) = 0.9. Find P(F |E).
Suppose that E and F are two events and P(E) = 0.9 and P(F |E) = 0.3. Find P(E and F ).
A real estate agent conducted a survey of 200 landlords and asked how long their apartments remained vacant before a tenant was found. The results of the survey are shown in the table. The data are based on information obtained from the U.S. Census Bureau.Duration of Vacancy ....FrequencyLess than
In how many ways can three men and three women be seated around a circular table (that seats six) assuming that women and men must alternate seats?
Payton’s futsal team consists of 10 girls, but only 5 can be on the field at any given time (four fielders and a goalie). (a) How many starting lineups are possible if all players are selected without regard to position played? (b) How many starting lineups are possible if either Payton or
The following data represent the survival data for the ill-fated Titanic voyage by gender. The males are adult males and the females are adult females.Suppose a passenger is selected at random. (a) What is the probability that the passenger survived? (b) What is the probability that the passenger
Use According to the Statistical Abstract of the United States, about 17% of all 18- to 25-year-olds are current marijuana users. (a) What is the probability that four randomly selected 18- to 25-year-olds are all marijuana users? (b) What is the probability that among four randomly selected 18- to
24 The distribution of National Honor Society members among the students at a local high school is shown in the table. A student€™s name is drawn at random.(a) What is the probability that the student is a junior? (b) What is the probability that the student is a senior, given that the
In 2002, Valerie Wilson won $1 million in a scratch-off game (Cool Million) from the New York lottery. Four years later, she won $1 million in another scratch-off game ($3,000,000 Jubilee), becoming the first person in New York state lottery history to win $1 million or more in a scratch-off game
In the game Text Twist, 6 letters are given and the player must form words of varying lengths using the letters provided. Suppose that the letters in a particular game are ENHSIC. (a) How many different arrangements are possible using all 6 letters? (b) How many different arrangements are possible
According to a survey by Pew Internet, 79% of teens own an iPod or other MP3 player. If the probability that both a teen and his or her parent own an iPod or other MP3 player is 0.430, what is the probability that a parent owns such a device given that his or her teenager owns one?
In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers corresponding to the numbers remaining on their Lingo board. There are also three prize balls and three red
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of students in a randomly selected elementary school classroom (b) The amount of snow that falls in Minneapolis during the winter season (c) The flight
Determine whether the distribution is a discrete probability distribution. If not, state why. (a) X ... P(x) 0 .... 0.34 1 .... 0.21 2 .... 0.13 3 .... 0.04 4 .... 0.01 (b) x .... P(x) 0 .... 0.40 1 .... 0.31 2 .... 0.23 3 .... 0.04 4 .... 0.02
The Stanley Cup is a best-of-seven series to determine the champion of the National Hockey League. The following data represent the number of games played, X, in the Stanley Cup before a champion was determined from 1939 to 2011.x ....Frequency4 ....205 ....176 ....197 ....16(a) Construct a
A popular casino table game is three-card poker. One aspect of the game is the €œpair plus€ bet in which a player is paid a dollar amount for any hand of a pair or better, regardless of the hand the dealer has. The table shows the proï¬t and probability of
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