Choosing Two Aces Two cards are selected at random,

In your words, explain the law of large numbers.

Explain how empirical probability can be used to determine whether a die is loaded (not a fair die).

Cars Of 45 people who purchase a vehicle at a car dealership, 9 purchased an SUV. Determine the empirical probability that the next person who purchases a vehicle from that car dealership purchases an SUV.

Cards Select a card from a deck of cards 40 times with replacement and compute the empirical probability of selecting a heart.

Television News In a small town, 250 people were asked whether they watched ABC, CBS, NBC, Fox, or MSNBC news. The results are indicated below. Determine the empirical probability that the next person selected at random from the town watches ABC news.

Digits In Exercises 69, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is written on a piece of paper and all the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is even

Digits In Exercises 69, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is written on a piece of paper and all the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is odd or greater than 3.

Digits In Exercises 69, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is written on a piece of paper and all the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is greater than 2 or less than 6.

Digits In Exercises 69, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is written on a piece of paper and all the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is even and greater than 4.

Yogurt Preference In Exercises 1013, a taste test is given to 50 customers at a supermarket. The customers are asked to taste 4 types of yogurt and to list their favorite. The results are summarized below. If one person who participated in the taste test is selected at random, determine the probability that the persons favorite was strawberry

Yogurt Preference In Exercises 1013, a taste test is given to 50 customers at a supermarket. The customers are asked to taste 4 types of yogurt and to list their favorite. The results are summarized below. If one person who participated in the taste test is selected at random, determine the probability that the persons favorite was blueberry

Yogurt Preference In Exercises 10-13, a taste test is given to 50 customers at a supermarket. The customers are asked to taste 4 types of yogurt and to list their favorite. The results are summarized below. If one person who participated in the taste test is selected at random, determine the probability that the persons favorite was either strawberry or raspberry.

Yogurt Preference In Exercises 1013, a taste test is given to 50 customers at a supermarket. The customers are asked to taste 4 types of yogurt and to list their favorite. The results are summarized below. If one person who participated in the taste test is selected at random, determine the probability that the persons favorite was a yogurt other than banana creme pie.

Obesity According to the U.S. Centers for Disease Control and Prevention, 20% of children in the United States,age 6 11, are obese. If a child age 611 was selected at random, determine the odds a) against the child being obese. b) in favor of the child being obese.

Vegetable Mix-up Nicholas Delaney, a mischievous little boy, has removed labels on the eight cans of vegetables in the cabinet. Nicholass father knows that there are three cans of corn, three cans of beans, and two cans of carrots. If the father selects and opens one can at random, determine the odds against his selecting a can of corn.

Horseracing The odds against Buttermilk winning the Triple Crown in horse racing are 82 : 3. Determine the probability that Buttermilk wins the Triple Crown.

Dry Cleaner Success The probability that a new dry cleaner will succeed at a given location is 0.85. Determine the odds in favor of the dry cleaner succeeding.

Raffle Tickets One thousand raffle tickets are sold at $2 each. Three prizes of $200 and two prizes of $100 will be awarded. Assume that the probability that any given ticket is selected for a $200 prize is 3 1000 and the probability that any given ticket is selected for a $100 prize is 2 1000. a) Determine the expectation of a person who purchases a ticket. b) Determine the expectation of a person who purchases three tickets.

Expectation of a Card If Cameron selects a picture card from a standard deck of 52 cards, Lindsey will give him $9. If Cameron does not select a picture card, he must give Lindsey $3. a) Determine Camerons expectation. b) Determine Lindseys expectation. c) If Cameron plays this game 100 times, how much can he expect to lose or gain?

Expected Attendance If the day is sunny, 1000 people will attend the baseball game. If the day is cloudy, only 500 people will attend. If it rains, only 100 people will attend. The local meteorologist states that the probability of a sunny day is 0.4, of a cloudy day is 0.5, and of a rainy day is 0.1. Determine the number of people that are expected to attend.

Fair Price At a game of chance, the expected value is found to be -$2.50, and the cost to play the game is $6.50. Determine the fair price to play the game.

Fair Price The expected value when you purchase a lottery ticket is - $1.50, and the cost to play the game is $5.00. Determine the fair price of the lottery ticket.

Club Officers Tina, Jake, Gina, and Carla form a club. They plan to select a president and a vice president. a) Construct a tree diagram showing all the possible outcomes. b) List the sample space. c) Determine the probability that Gina is selected president and Jake is selected vice president.

A Coin and a Number A coin is flipped and then a number from 1 through 4 is selected at random from a bag. a) Construct a tree diagram showing all the possible outcomes. b) List the sample space. c) Determine the probability that a head is flipped and an odd number is selected. d) Determine the probability that a head is flipped or an odd number is selected.

Spinning Two Wheels In Exercises 2530, the outer and inner wheels are spun. 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3 Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining even numbers on both wheels.

Spinning Two Wheels In Exercises 2530, the outer and inner wheels are spun. 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3 Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining numbers greater than 5 on both wheels.

Spinning Two Wheels In Exercises 2530, the outer and inner wheels are spun. 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3 Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining an odd number on the outer wheel and a number less than 6 on the inner wheel.

Spinning Two Wheels In Exercises 2530, the outer and inner wheels are spun. 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3 Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining an even number or a number less than 6 on the outer wheel.

Spinning Two Wheels In Exercises 2530, the outer and inner wheels are spun. 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3 Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining an even number or a color other than green on the inner wheel.

Spinning Two Wheels In Exercises 2530, the outer and inner wheels are spun. 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3 Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining gold on the outer wheel and a color other than gold on the inner wheel.

Sports Drink Selection In Exercises 3134, assume that Skip Bailey is going to purchase three bottles of sports drinks at a convenience store. The store has 12 different bottles of sports drinks, including 5 different bottles made by Gatorade, 4 different bottles made by Powerade, and 3 different bottles made by All Sport. If Skip selects 3 of these 12 bottles at random, determine the probability he selects 3 bottles of Gatorade.

Sports Drink Selection In Exercises 3134, assume that Skip Bailey is going to purchase three bottles of sports drinks at a convenience store. The store has 12 different bottles of sports drinks, including 5 different bottles made by Gatorade, 4 different bottles made by Powerade, and 3 different bottles made by All Sport. If Skip selects 3 of these 12 bottles at random, determine the probability he selects no bottles of Powerade.

Sports Drink Selection In Exercises 3134, assume that Skip Bailey is going to purchase three bottles of sports drinks at a convenience store. The store has 12 different bottles of sports drinks, including 5 different bottles made by Gatorade, 4 different bottles made by Powerade, and 3 different bottles made by All Sport. If Skip selects 3 of these 12 bottles at random, determine the probability he selects at least 1 bottle of Powerade.

Sports Drink Selection In Exercises 3134, assume that Skip Bailey is going to purchase three bottles of sports drinks at a convenience store. The store has 12 different bottles of sports drinks, including 5 different bottles made by Gatorade, 4 different bottles made by Powerade, and 3 different bottles made by All Sport. If Skip selects 3 of these 12 bottles at random, determine the probability he selects a bottle of Gatorade, a bottle of Gatorade, and a bottle of All Sport, in that order.

Spinner Probabilities In Exercises 3538, assume that the spinner cannot land on a line. If spun once, determine the probability that the spinner lands on yellow.

Spinner Probabilities In Exercises 3538, assume that the spinner cannot land on a line. If spun once, determine the odds against and the odds in favor of the spinner landing on yellow.

Spinner Probabilities In Exercises 3538, assume that the spinner cannot land on a line. If spun once, determine You are awarded $5 if the spinner lands on red, $10 if it lands on yellow, and $20 if it lands on green. Determine your expected value.

Spinner Probabilities In Exercises 3538, assume that the spinner cannot land on a line. If spun once, determine If the spinner is spun twice, determine the probability that it lands on red and then green (assume independence).

Spinner Probabilities In Exercises 3942, assume that the spinner cannot land on a line. If spun once, determine the probability that the spinner does not land on green.

Spinner Probabilities In Exercises 39-42, assume that the spinner cannot land on a line. If spun once, determine the odds in favor of and the odds against the spinner landing on green.

Spinner Probabilities In Exercises 39-42, assume that the spinner cannot land on a line. If spun once, determine A person wins $10 if the spinner lands on green, wins $5 if the spinner lands on red, and loses $20 if the spinner lands on yellow. Find the expectation of a person who plays this game.

Spinner Probabilities In Exercises 3942, assume that the spinner cannot land on a line. If spun once, determine If the spinner is spun three times, determine the probability that at least one spin lands on red.

Restaurant Service In Exercises 43 46, use the results of a survey regarding the service at the Lake View Diner, which is summarized as follows. Meal Service Rated Good Service Rated Poor Total Breakfast 85 10 95 Lunch 65 10 75 Total 150 20 170 If one person who completed the survey is selected at random, determine the probability that the person indicated that the service was rated good.

Restaurant Service In Exercises 43 46, use the results of a survey regarding the service at the Lake View Diner, which is summarized as follows. Meal Service Rated Good Service Rated Poor Total Breakfast 85 10 95 Lunch 65 10 75 Total 150 20 170 If one person who completed the survey is selected at random, determine the probability that the person indicated that the service was rated good, given that the meal was breakfast.

Restaurant Service In Exercises 43 46, use the results of a survey regarding the service at the Lake View Diner, which is summarized as follows. Meal Service Rated Good Service Rated Poor Total Breakfast 85 10 95 Lunch 65 10 75 Total 150 20 170 If one person who completed the survey is selected at random, determine the probability that the person indicated that the service was rated poor, given that the meal was lunch.

Restaurant Service In Exercises 43 46, use the results of a survey regarding the service at the Lake View Diner, which is summarized as follows. Meal Service Rated Good Service Rated Poor Total Breakfast 85 10 95 Lunch 65 10 75 Total 150 20 170 If one person who completed the survey is selected at random, determine the probability that the person indicated that the meal was breakfast, given that the service was rated poor.

Neuroscience In Exercises 4750, assume that in a neuroscience course the students perform an experiment. Tests are given to determine if people are right brained, are left brained, or have no predominance. It is also recorded whether they are right handed or left handed. The following chart shows the results obtained. If one person who completed the survey is selected at random, determine the probability the person selected is right handed.

Neuroscience In Exercises 4750, assume that in a neuroscience course the students perform an experiment. Tests are given to determine if people are right brained, are left brained, or have no predominance. It is also recorded whether they are right handed or left handed. The following chart shows the results obtained. If one person who completed the survey is selected at random, determine the probability the person selected is left brained, given that the person is left handed.

Neuroscience In Exercises 4750, assume that in a neuroscience course the students perform an experiment. Tests are given to determine if people are right brained, are left brained, or have no predominance. It is also recorded whether they are right handed or left handed. The following chart shows the results obtained. If one person who completed the survey is selected at random, determine the probability the person selected is right handed, given that the person has no predominance.

Neuroscience In Exercises 4750, assume that in a neuroscience course the students perform an experiment. Tests are given to determine if people are right brained, are left brained, or have no predominance. It is also recorded whether they are right handed or left handed. The following chart shows the results obtained. If one person who completed the survey is selected at random, determine the probability the person selected is right brained, given that the person is left handed.

Television Show Four contestants are on a television show. There are four different-colored rubber balls in a box, and each contestant gets to pick one from the box. Inside each ball is a slip of paper indicating the amount the contestant has won. The amounts are $10,000, $5000, $2000, and $1000. a) In how many different ways can the contestants select the balls? b) What is the expectation of a contestant?

Spelling Bee Five finalists remain in a high school spelling bee. Two will receive $50 each, two will receive $100 each, and one will receive $500. How many different arrangements of prizes are possible?

Candy Selection Mrs. Williams takes her 3 children shopping. Each of her children gets to select a different type of candy that only that child will eat. At the store, there are only 10 boxes of candy left and each is a different type. In how many ways can the 3 children select the candy

Astronaut Selection Three of nine astronauts must be selected for a mission. One will be the captain, one will be the navigator, and one will perform scientific experiments. Assuming each of the nine astronauts can perform any of the tasks, in how many ways can a three-person crew be selected so that each person has a different assignment?

Vaccine Dr. Goldberg has three doses of vaccine for influenza type A. Six patients in the office require the vaccine. In how many different ways could Dr. Goldberg dispense the vaccine?

Dogsled Ten huskies are to be selected to pull a dogsled. How many different arrangements of the 10 huskies on a dogsled are possible?

Mega Millions To play the lottery game Mega Millions, you select 5 numbers from 1 through 56 and 1 Mega Ball number from 1 through 46. If you match all 6 numbers, you win the jackpot! + Mega Millions win Select Mega Ball number from 146 Select 5 numbers from 156 a) What is the probability that you match the first 5 numbers? b) What is the probability that you match the first 5 numbers and the Mega Ball?

Parent-Teacher Committee A committee of 7 is to be formed from 10 parents and 12 teachers. If the committee is to consist of 2 parents and 5 teachers, how many different committees are possible?

Selecting Test Subjects In a psychology research laboratory, one room contains eight men and another room contains five women. Three men and two women are to be selected at random to be given a psychological test. How many different combinations of these people are possible?

Choosing Two Aces Two cards are selected at random, without replacement, from a standard deck of 52 cards. Determine the probability that two aces are selected (use combinations).

Color Chips In Exercises 61 64, a bag contains five red chips, three white chips, and two blue chips. Three chips are to be selected at random, without replacement. Determine the probability that all are red.

Color Chips In Exercises 61 64, a bag contains five red chips, three white chips, and two blue chips. Three chips are to be selected at random, without replacement. Determine the probability that the first two are red and the third is blue.

Color Chips In Exercises 61 64, a bag contains five red chips, three white chips, and two blue chips. Three chips are to be selected at random, without replacement. Determine the probability that the first is red, the second is white, and the third is blue.

Color Chips In Exercises 61 64, a bag contains five red chips, three white chips, and two blue chips. Three chips are to be selected at random, without replacement. Determine the probability that at least one is red.

Magazines In Exercises 65 68, on a table in a doctors office are five Newsweek magazines, six Parenting magazines, and three Sports Illustrated magazines. If Ramona Cleary randomly selects three magazines, determine the probability that three Newsweek magazines were selected.

Magazines In Exercises 65-68, on a table in a doctors office are five Newsweek magazines, six Parenting magazines, and three Sports Illustrated magazines. If Ramona Cleary randomly selects three magazines, determine the probability that two Parenting magazines and one Sports Illustrated magazine were selected.

Magazines In Exercises 65 68, on a table in a doctors office are five Newsweek magazines, six Parenting magazines, and three Sports Illustrated magazines. If Ramona Cleary randomly selects three magazines, determine the probability that no Parenting magazine was selected.

Magazines In Exercises 65-68, on a table in a doctors office are five Newsweek magazines, six Parenting magazines, and three Sports Illustrated magazines. If Ramona Cleary randomly selects three magazines, determine the probability that at least one Parenting magazine was selected.

New Homes In the community of Spring Hill, 60% of the homes purchased cost more than $160,000. a) Write the binomial probability formula to determine the probability that exactly x of the next n homes purchased in Spring Hill cost more than $160,000 b) Write the binomial probability formula to determine the probability that exactly 75 of the next 100 home purchases cost more than $160,000.

Long-Stemmed Roses At the Floyds Flower Shop, 1 5 of people ordering flowers select long-stemmed roses. Determine the probability that exactly 3 of the next 5 customers ordering flowers select long-stemmed roses.

Taking a Math Course During any semester at City College, 60% of the students are taking a mathematics course. Determine the probability that of five students selected at random, a) none is taking a mathematics course this semester. b) at least one is taking a mathematics course this semester.

Flowers Of the last 50 people who purchased flowers at Whistlestop Florist, 14 purchased roses. Determine the empirical probability that the next person who purchases flowers at Whistlestop Florist purchases roses.

One Sheet of Paper In Exercises 2 4, each of the numbers 19 is written on a sheet of paper and the nine sheets of paper are placed in a hat. If one sheet of paper is selected at random from the hat, determine the probability that the number selected is greater than 4.

One Sheet of Paper In Exercises 2 4, each of the numbers 19 is written on a sheet of paper and the nine sheets of paper are placed in a hat. If one sheet of paper is selected at random from the hat, determine the probability that the number selected is even.

One Sheet of Paper In Exercises 2 4, each of the numbers 19 is written on a sheet of paper and the nine sheets of paper are placed in a hat. If one sheet of paper is selected at random from the hat, determine the probability that the number selected is even or greater than 5.

Two Sheets of Paper In Exercises 57, if two of the same nine sheets of paper mentioned above are selected, without replacement, from the hat, determine the probability that both numbers are greater than 5.

Two Sheets of Paper In Exercises 57, if two of the same nine sheets of paper mentioned above are selected, without replacement, from the hat, determine the probability that the first number is odd and the second number is even.

Two Sheets of Paper In Exercises 57, if two of the same nine sheets of paper mentioned above are selected, without replacement, from the hat, determine the probability that neither of the numbers is greater than 6.

Two Sheets of Paper In Exercises 57, if two of the same nine sheets of paper mentioned above are selected, without replacement, from the hat, determine the probability that One card is selected at random from a standard deck of 52 cards. Determine the probability that the card selected is a red card or a picture card.

One Chip and One Die In Exercises 9-13, one colored chipred, blue, or greenis selected at random and a die is rolled.Use the counting principle to determine the number of sample points in the sample space.

One Chip and One Die In Exercises 913, one colored chipred, blue, or greenis selected at random and a die is rolled.Construct a tree diagram illustrating all the possible outcomes and list the sample space.

In Exercises 1113, by observing the sample space of the chips and die, determine the probability of obtaining the color green and the number 2.

In Exercises 1113, by observing the sample space of the chips and die, determine the probability of obtaining the color red or the number 1.

In Exercises 1113, by observing the sample space of the chips and die, determine the probability of obtaining a color other than red or an even number.

Passwords A personal password for an Internet brokerage account is to consist of a letter, followed by two digits, followed by two letters. Determine the number of personal codes possible if the first digit cannot be zero and repetition is permitted.

Puppies A litter of collie puppies consists of four males and five females. If one of the puppies is selected at random, determine the odds a) against the puppy being male. b) in favor of the puppy being female.

Pick a Card You get to select one card at random from a standard deck of 52 cards. If you pick a club, you win $8. If you pick a heart, you win $4. If you pick any other suit, you lose $6. Determine your expectation for this game.

Cars and SUVs The number of cars and the number of SUVs going through the toll gates of two bridges is recorded. The results are shown below. Bridge Cars SUVs Total George Washington 120 106 226 Golden Gate 94 136 230 Total 214 242 456 A toll booth at the Golden Gate Bridge If one of these vehicles going over the bridges is selected at random, determine the probability that a) it is a car.b) it is going over the George Washington Bridge. c) it is an SUV, given that it is going over the George Washington Bridge. d) it is going over the Golden Gate Bridge, given that it is a car.

Awarding Prizes Three of six people are to be selected and given small prizes. One will be given a book, one will be given a calculator, and one will be given an iTunes card. In how many different ways can these prizes be awarded?

Quality Control A bin contains a total of 20 batteries, of which 6 are defective. If you select 2 at random, without replacement, determine the probability that a) none of the batteries is good. b) at least one battery is good.

University Admission The probability that a person is accepted for admission to a specific university is 0.6. Determine the probability that exactly two of the next five people who apply to the university get accepted.

Your cars speedometer indicates that you are traveling at 65 mph. What is the probability that you are traveling at exactly 65 mph? Explain your answer.

A 10-question multiple-choice exam is given, and each question has five possible answers. Pascal Gonyo takes this exam and guesses at every question. Use the binomial probability formula to determine the probability (to 5 decimal places) that a) he gets exactly 2 questions correct. b) he gets no questions correct. c) he gets at least 1 question correct (use the information from part (b) to answer this part). d) he gets at least 9 questions correct. e) Without using the binomial probability formula, determine the probability that he gets exactly 2 questions correct. f ) Compare your answers to parts (a) and (e). If they are not the same, explain why.

Many cars have keyless entry. To open the lock, you may press a 5-digit code on a set of buttons like that illustrated. The code may include repeated digits like 11433 or 55512. 1 - 2 3 - 4 5 - 6 7 - 8 9 - 0 a) How many different 5-digit codes can be made using the 10 digits if repetition is permitted? b) How many different ways are there of pressing 5 buttons if repetition is allowed? c) A burglar is going to press 5 buttons at random, with repetition allowed. What is the probability that the burglar hits the sequence to open the door? d) Suppose that each button had only one number associated with it as illustrated below. How many different 5-digit codes can be made with the 5 digits if repetition is permitted? 12345 e) Using the buttons labeled 15, how many different ways are there to press 5 buttons if repetition is allowed? f ) A burglar is going to press 5 buttons of those labeled 15 at random with repetition allowed. Determine the probability that the burglar hits the sequence to open the door. g) Is a burglar more likely, is he or she less likely, or does he or she have the same likelihood of pressing 5 buttons and opening the car door if the buttons are labeled as in the first illustration or as in the second illustration? Explain your answer. h) Can you see any advantages in labeling the buttons as in the first illustration? Explain.*