Solution: In Exercises 918, the problems are to be done without replacement. Use

A controlled operation that yields a set of results is called a(n) .

The possible results of an experiment are called its .

A subcollection of the outcomes of an experiment is called a(n) .

Probability is classified as either theoretical probability or probability.

Probability determined by the relative frequency of occurrence of an event, or actual observations of an experiment is called probability.

Probability determined through a study of the possible outcomes that can occur for a given experiment is called probability.

Flip a Coin Flip a coin 50 times and record the results. Determine the empirical probability of flipping a) a head. b) a tail. c) Does the probability of flipping a head appear to be the same as flipping a tail?

Pair of Dice Roll a pair of dice 60 times and record the sums. Determine the empirical probability of rolling a sum of a) 2. b) 7. c) Does the probability of rolling a sum of 2 appear to be the same as the probability of rolling a sum of 7?

Roll a Die Roll a die 50 times and record the results. Determine the empirical probability of rolling a) a 1. b) a 4. c) Does the probability of rolling a 1 appear to be the same as the probability of rolling a 4? Explain.

Two Coins Flip two coins 50 times and record the number of times exactly one head was obtained. Determine the empirical probability of flipping exactly one head.

Boat Rentals The last 30 boat rentals at Green Lakes Boat Rentals were 14 sunfish, 10 kayaks, and 6 rowboats. Use this information to determine the empirical probability that the next boat rental is a a) sunfish. b) kayak. c) rowboat.

Music Purchases At the Virgin Music store in Times Square, 60 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 60, 12 chose rock, 16 chose country, 8 chose classical, and 24 chose something other than rock, country, or classical. Determine the empirical probability that the next person entering the store favors a) rock music. b) country music. c) something other than rock, country, or classical music.

Veterinarian In a given week, a veterinarian treated the following animals. Determine the empirical probability that the next animal she treats is a) a dog. b) a cat. c) a rabbit.

PraderWilli Syndrome In a sample of 50,000 first-born babies, 5 were found to have PraderWilli syndrome. Find the empirical probability that a familys first child will be born with this syndrome.

Studying Abroad The table below shows the 10 most popular destinations for U.S. college students studying abroad for the 20082009 school year.If a student were selected at random from those who studied abroad in 20082009 at one of the destinations in the table, determine the empirical probability that the student studied in a) China. b) Italy. c) Australia

Travel Web Sites The following table shows the number of visitors to the five most frequently visited travel Web sites in October 2010. Assuming this trend continues, if a person chooses to visit only one of the listed Web sites, determine the empirical probability the person will visit a) Priceline. b) Expedia. c) Trip Advisor

Top-Selling Video Games The following table shows the number of video games sold worldwide for the five highest-selling video games in 2010. Assuming this trend continues, if a person chooses to purchase a video game, determine the empirical probability that the person will purchase a) Wii Sports. b) Wii Fit Plus. c) Call of Duty: Black Ops.

Grade Distribution Mr. Dooles grade distribution over the past 3 years for a course in college algebra is shown in the chart below. If Sue Gilligan plans to take college algebra with Mr. Doole, determine the empirical probability that she receives a grade of a) A. b) C. c) D or higher.

Election In an election for student council president at Russell Sage College, 80 students were polled and asked for whom they planned to vote. The table shows the results of the poll. If one student from Russell Sage College is selected at random, determine the empirical probability that the person planned to vote for a) Allison. b) Emily. c) Kimberly. d) Johanna. e) Someone other than the four people-listed above.

Volunteer Hours The graph below shows the average number of hours volunteered per week by Americans in 2009. Average Number of Hours Americans Volunteered per Week 1 or less 50% Between 1 and 2 16% Between 2 and 5 17% More than 5 12% Not reported 5% Source: CNCS (www.serve.gov)If one American who participated in volunteer work is selected at random, determine the empirical probability the person volunteered a) between 1 and 2 hours per week. b) more than 5 hours per week. c) between 2 and 5 hours per week.

Hitting a Bulls-Eye The pattern of hits shown on the target resulted from a marksman firing 20 rounds. For a single shot, a) determine the empirical probability that the marksman hits the 50-point bulls-eye (the center of the target). b) determine the empirical probability that the marksman does not hit the bulls-eye. c) determine the empirical probability that the marksman scores at least 20 points. d) determine the empirical probability that the marksman does not score any points (the area outside the large circle).

Rock Toss Jim Handy finds an irregularly shaped five-sided rock. He labels each side and tosses the rock 100 times. The results of his tosses are shown in the table. Determine the empirical probability that the rock will land on side 4 if tossed again.

Cell Biology Experiment An experimental serum was injected into 500 guinea pigs. Initially, 150 of the guinea pigs had circular cells, 250 had elliptical cells, and 100 had irregularly shaped cells. After the serum was injected, none of the guinea pigs with circular cells were affected, 50 with elliptical cells were affected, and all those with irregular cells were affected. Determine the empirical probability that a guinea pig with (a) circular cells, (b) elliptical cells, and (c) irregular cells will be affected by injection of the serum.

In a large hall there are 325 students out of which 160 are male and 165 are female. If one student is selected at random, determine the empirical probability that the individual selected is (a) male. (b) female.

Mendels Experiment In one of his experiments (see pages 677678), Mendel crossbred nonpure purple flower pea plants. These purple pea plants had two traits for flowers, purple (dominant) and white (recessive). The result of this crossbreeding was 705 second-generation plants with purple flowers and 224 second-generation plants with white flowers. Determine the empirical probability of a second-generation plant having a) white flowers. b) purple flowers.

Second-Generation Offspring In another experiment, Mendel crossbred nonpure tall pea plants. As a result, the second-generation offspring were 787 tall plants and 277 short plants. Determine the empirical probability of a second-generation plant being a) tall. b) short.

The theoretical probability of a coin landing heads up is 1 2. Does this probability mean that if a coin is flipped two times, one flip will land heads up? If not, what does it mean?

To determine premiums, life insurance companies must compute the probable date of death. On the basis of a great deal of research, Mr. Duncan, age 36, is expected to live another 43.21 years. Does this determination mean that Mr. Duncan will live until he is 79.21 years old? If not, what does it mean?

a) Explain how you would find the empirical probability of rolling a 5 on a die. b) What do you believe is the empirical probability of rolling a 5? c) Determine the empirical probability of rolling a 5 by rolling a die 40 times.

a) Explain how you would find the empirical probability of rolling a 5 on a die. b) What do you believe is the empirical probability of rolling a 5? c) Determine the empirical probability of rolling a 5 by rolling a die 40 times.

The theoretical probability of rolling a 4 on a die is 1 6. Does this probability mean that if a die is rolled six times one 4 will appear? If not, what does it mean?

1. a) Design an Experiment Which do you believe is used more frequently in a magazine or newspaper article, the word a or the word the?b) Design an experiment to determine the empirical probabilities (or relative frequencies) of the words a and the appearing in a magazine or newspaper article. c) Perform the experiment in part (b) and determine the empirical probabilities. d) Which word, a or the, appears to occur more frequently?

Cola Preference Can people selected at random distinguish Coke from Pepsi? Which do they prefer? a) Design an experiment to determine the empirical probability that a person selected at random can select Coke when given samples of both Coke and Pepsi. b) Perform the experiment in part (a) and determine the empirical probability. c) Determine the empirical probability that a person selected at random will prefer Coke over Pepsi.

Write a paper on how insurance companies use empirical probabilities in determining insurance premiums. An insurance agent may be able to direct you to a source of information.

Write a paper on how Gregor Mendels use of empirical probability led to the development of the science of genetics. You may want to check with a biology professor to determine references to use.

Ten red balls and four blue balls are in a bag. If four balls from the bag are to be selected at random, determine the probability of selecting four red balls.

A class consists of 15 girls and 12 boys. If 8 of the students are to be selected at random, determine the probability that they are all girls.

Three letters are to be selected at random from the English alphabet of 26 letters. Determine the probability that 3 vowels (a, e, i, o, u) are selected.

Determine the probability of being dealt 3 aces from a standard deck of 52 cards when 3 cards are dealt

A dog breeder has 15 puppies for sale, of which 8 are yellow Labrador retrievers. If 5 puppies are selected at random, determine the probability they are all yellow Labrador retrievers.

Of 80 people attending a dance, 28 have a college degree. If 4 people at the dance are selected at random, determine the probability that each of the 4 has a college degree.

Of 120 students attending a college orientation session, 23 are criminal justice majors. If 5 students at the orientation are selected at random, determine the probability that each of the 5 is a criminal justice major.

A class of 16 people contains 4 people whose birthday is in October. If 3 people from the class are selected at random, determine the probability that none of those selected has an October birthday.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Selecting Lightbulbs A box contains 3 defective and 7 good lightbulbs. If two lightbulbs are to be selected at random from the box, determine the probability that both lightbulbs are defective.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Green and Red Balls A bag contains four red balls and five green balls. You plan to select three balls at random. Determine the probability of selecting three green balls.

In Exercises 9-18, the problems are to be done without replacement. Use combinations to determine probabilities. Flu Vaccine A doctor has five doses of flu protection vaccine left. He has six women and eight men who want the medication. If the names of five of these people are selected at random, determine the probability that five men's names are selected.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Bills of Four Denominations Duc Trans wallet contains 8 bills of the following denominations: four $5 bills, two $10 bills, one $20 bill, and one $50 bill. If Duc selects two bills at random, determine the probability that he selects two $5 bills.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Selecting Digits Each of the digits 09 is written on a slip of paper, and the slips are placed in a hat. If three slips of paper are selected at random, determine the probability that the three numbers selected are greater than 5.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Selecting Books Barnes & Noble has 20 different books listed on its clearance list. Twelve books are listed as mystery, and 8 are listed as romance. If 4 books are selected at random from the list, determine the probability that they are all mystery books.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Gift Certificates The sales department at Atwell Studios consists of three people, the manufacturing department consists of six people, and the accounting department consists of two people. Three people will be selected at random from these people and will be given gift certificates to Sweet Tomatoes, a local restaurant. Determine the probability that two of those selected will be from the manufacturing department and one will be from the accounting department.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Faculty-Student Committee A committee of four is to be randomly selected from a group of seven teachers and eight students. Determine the probability that the committee will consist of two teachers and two students.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Winning the Grand Prize A lottery consists of 46 numbers. You select 6 numbers, and if they match the 6 numbers selected by the lottery commission, you win the grand prize. Determine the probability of winning the grand prize.

In Exercises 918, the problems are to be done without replacement. Use combinations to determine probabilities. Red Cards You are dealt 5 cards from a standard deck of 52 cards. Determine the probability that you are dealt 5 red cards.

TV Game Show In Exercises 1922, a television game show has five doors, of which the contestant must pick two. Behind two of the doors are expensive cars, and behind the other three doors are consolation prizes. The contestant gets to keep the items behind the two doors she selects. Determine the probability that the contestant wins no cars.

TV Game Show In Exercises 1922, a television game show has five doors, of which the contestant must pick two. Behind two of the doors are expensive cars, and behind the other three doors are consolation prizes. The contestant gets to keep the items behind the two doors she selects. Determine the probability that the contestant wins both cars.

TV Game Show In Exercises 1922, a television game show has five doors, of which the contestant must pick two. Behind two of the doors are expensive cars, and behind the other three doors are consolation prizes. The contestant gets to keep the items behind the two doors she selects. Determine the probability that the contestant wins at least one car.

TV Game Show In Exercises 1922, a television game show has five doors, of which the contestant must pick two. Behind two of the doors are expensive cars, and behind the other three doors are consolation prizes. The contestant gets to keep the items behind the two doors she selects. Determine the probability that the contestant wins exactly one car.

Baseball In Exercises 2326, assume that a particular professional baseball team has 10 pitchers, 6 infielders, and 9 other players. If 3 players names are selected at random, determine the probability that all 3 are infielders.

Baseball In Exercises 2326, assume that a particular professional baseball team has 10 pitchers, 6 infielders, and 9 other players. If 3 players names are selected at random, determine the probability that none of the three is a pitcher.

Baseball In Exercises 2326, assume that a particular professional baseball team has 10 pitchers, 6 infielders, and 9 other players. If 3 players names are selected at random, determine the probability that 2 are pitchers and 1 is an infielder.

Baseball In Exercises 2326, assume that a particular professional baseball team has 10 pitchers, 6 infielders, and 9 other players. If 3 players names are selected at random, determine the probability that 1 is a pitcher and 2 are players other than pitchers and infielders.

Car Rental In Exercises 27-30, a car rental agency has 10 midsized and 15 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, determine the probability (as a decimal number rounded to four decimal places) that the cars selected consist of all midsized cars.

Car Rental In Exercises 2730, a car rental agency has 10 midsized and 15 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, determine the probability (as a decimal number rounded to four decimal places) that the cars selected consist of 2 midsized cars and 4 compact cars.

Car Rental In Exercises 27-30, a car rental agency has 10 midsized and 15 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, determine the probability (as a decimal number rounded to four decimal places) that the cars selected consist of 3 midsized cars and 3 compact cars.

Car Rental In Exercises 2730, a car rental agency has 10 midsized and 15 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, determine the probability (as a decimal number rounded to four decimal places) that the cars selected consist of at least 1 compact car.

New Soup In Exercises 3134, Campbells is testing 12 new soups for possible production. They are testing 3 Chunky soups, 4 Healthy Request soups, and 5 Select Harvest soups. If we assume each of the 12 soups has the same chance of being selected and 4 new soups will be produced, determine the probability that the four new soups selected will be as follows 2 are Healthy Request soups and 2 are Chunky soups.

New Soup In Exercises 3134, Campbells is testing 12 new soups for possible production. They are testing 3 Chunky soups, 4 Healthy Request soups, and 5 Select Harvest soups. If we assume each of the 12 soups has the same chance of being selected and 4 new soups will be produced, determine the probability that the four new soups selected will be as follows 3 are Select Harvest soups and 1 is a Healthy Request soup.

New Soup In Exercises 3134, Campbells is testing 12 new soups for possible production. They are testing 3 Chunky soups, 4 Healthy Request soups, and 5 Select Harvest soups. If we assume each of the 12 soups has the same chance of being selected and 4 new soups will be produced, determine the probability that the four new soups selected will be as follows 1 is a Healthy Request soup, 1 is a Select Harvest soup, and 2 are Chunky soups.

New Soup In Exercises 31-34, Campbells is testing 12 new soups for possible production. They are testing 3 Chunky soups, 4 Healthy Request soups, and 5 Select Harvest soups. If we assume each of the 12 soups has the same chance of being selected and 4 new soups will be produced, determine the probability that the four new soups selected will be as follows at least one is a Chunky soup.

Theater In Exercises 3538, five men and six women are going to be assigned to a specific row of seats in a theater. If the 11 tickets for the numbered seats are given out at random, determine the probability that five women are given the first five seats next to the center aisle.

Theater In Exercises 3538, five men and six women are going to be assigned to a specific row of seats in a theater. If the 11 tickets for the numbered seats are given out at random, determine the probability that at least one woman is in one of the first five seats.

Theater In Exercises 3538, five men and six women are going to be assigned to a specific row of seats in a theater. If the 11 tickets for the numbered seats are given out at random, determine the probability that exactly one woman is in one of the first five seats.

Theater In Exercises 3538, five men and six women are going to be assigned to a specific row of seats in a theater. If the 11 tickets for the numbered seats are given out at random, determine the probability that three women are seated in the first three seats and two men are seated in the next two seats.

Working Overtime Of 24 employees at Lowes home improvement store, 10 work as cashiers and 14 stock shelves. If 3 of the 24 employees are selected at random to work overtime, determine the probability that all 3 are cashiers.

Poker Probability A full house in poker consists of three of one kind and two of another kind in a five-card hand. For example, if a hand contains three kings and two 5s, it is a full house. If 5 cards are dealt at random from a standard deck of 52 cards, without replacement, determine the probability of getting three kings and two 5s.

A Royal Flush A royal flush consists of an ace, king, queen, jack, and 10 all in the same suit. If 7 cards are dealt at random from a standard deck of 52 cards, determine the probability of getting a a) royal flush in spades. b) royal flush in any suit.

Restaurant Staff The staff of a restaurant consists of 25 people, including 8 waiters, 12 waitresses, and 5 cooks. For Mothers Day, a total of 9 people will need to be selected to work. If the selections are made at random, determine the probability that 3 waiters, 4 waitresses, and 2 cooks will be selected.

Dead Mans Hand A pair of aces and a pair of 8s is often known as a dead mans hand. (See the Did You Know? on page 753.) a) Determine the probability of being dealt a dead mans hand (any two aces, any two 8s, and one other card that is not an ace or an 8) when 5 cards are dealt, without replacement, from a standard deck of 52 cards. b) The actual cards Wild Bill Hickok was holding when he was shot were the aces of spades and clubs, the 8s of spades and clubs, and the 9 of diamonds. If you are dealt five cards without replacement, determine the probability of being dealt this exact hand.

Alternate Seating If three men and three women are to be assigned at random to six seats in a row at a theater, determine the probability that they will alternate by gender.

Selecting Officers A club consists of 15 people including Ali, Kendra, Ted, Alice, Marie, Dan, Linda, and Frank. From the 15 members, a president, vice president, and treasurer will be selected at random. An advisory committee of 5 other individuals will also be selected at random. a) Determine the probability that Ali is selected president, Kendra is selected vice president, Ted is selected treasurer, and the other 5 individuals named form the advisory committee. b) Determine the probability that 3 of the 8 individuals named are selected for the three officers positions and the other 5 are selected for the advisory board.

A Marked Deck A number is written with a magic marker on each card of a deck of 52 cards. The number 1 is put on the first card, 2 on the second, and so on. The cards are then shuffled and cut. What is the probability that the top 4 cards will be in ascending order? (For example, the top card is 12, the second 22, the third 41, and the fourth 51.)

Hair When the Isle of Flume took its most recent census, the population was 100,002 people. Nobody on the isle has more than 100,001 hairs on his or her head. Determine the probability that at least two people have exactly the same number of hairs on their head.