Banquet Meal Choices For a banquet, a committee can select

Determine whether each statement is true or false. If the statement is false, explain why. Subjective probability has little use in the real world.

When a standard die is rolled, find the probability of getting a. A 5 b. A number larger than 2 c. An odd number

Problem 2DP Sports and Leisure When poker games are shown on television, there are often percentages displayed that show how likely it is that a certain hand will win. Investigate how these percentages are determined. Show an example with two competing hands in a Texas Hold ’Em game. Include the percentages that each hand will win after the deal, the flop, the turn, and the river.

Problem 1CTC Con Man Game Consider this problem: A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has been specially made, and on each side it has a tail. Finally, a third coin has a head and a tail on it All coins are of the same denomination. The con man places the 3 coins in his pocket, selects one, and shows you one side. It is heads. He is willing to bet you even money that it is the two-headed coin. His reasoning is that it can’t be the two-tailed coin since a head is showing; therefore, there is a 50-50 chance of it being the two-headed coin. Would you take the bet? (Hint: See Exercise 1 in Data Projects.)

Problem 2CTC de Méré Dice Game Chevalier de Méré won money when he bet unsuspecting patrons that in 4 rolls of I die. he could get at least one 6; but he lost money when he bet that in 24 rolls of 2 dice, he could get at least a double 6. Using the probability rules, find the probability of each event and explain why he won the majority of the time on the first game but lost the majority of the time when playing the second game. (Hint: Find the probabilities of losing each game and subtract from 1.)

Problem 1DP Business and FinanceSelect a pizza restaurant and a sandwich shop. For the pizza restaurant look at the menu to determine how many sizes, crust types, and toppings are available. How many different pizza types are possible? For the sandwich shop determine how many breads, meats, veggies, cheeses, sauces, and condiments are available. How many different sandwich choices are possible?

Problem 2CQ Determine whether each statement is true or false. If the statement is false, explain why Classical probability uses a frequency distribution to compute probabilities.

Selecting a Card When a card is selected from a deck, find the probability of getting a. A club b. A face card or a heart c. A 6 and a spade d. A king e. A red card

Determine whether each statement is true or false. If the statement is false, explain why In classical probability, all outcomes in the sample space are equally likely.

Technology A music player or music organization program can keep track of how many different artists are in a library. First note how many different artists are in your music library. Then find the probability that if 25 songs are selected at random, none will have the same artist.

Determine whether each statement is true or false. If the statement is false, explain why. When two events are not mutually exclusive, P(A or B) = P(A) + P(B).

Problem 3RE Software Selection The top-10 selling computer software titles last year consisted of 3 for doing taxes, 5 antivirus or security programs, and 2 “others.” Choose on title at random. a. What is the probability that it is not used for doing taxes? b. What is the probability that it is used for taxes or is one of the “other” programs? (4–1) Source: www.infoplease.com

Classical Birthday Problem How many people do you think need to be in a room so that 2 people will have the same birthday (month and day)? You might think it is 366. This would, of course, guarantee it (excluding leap year), but how many people would need to be in a room so that there would be a 90% probability that 2 people would be born on the same day? What about a 50% probability? Actually, the number is much smaller than you may think. For example, if you have 50 people in a room, the probability that 2 people will have the same birthday is 97%. If you have 23 people in a room, there is a 50% probability that 2 people were born on the same day! The problem can be solved by using the probability rules. It must be assumed that all birthdays are equally likely, but this assumption will have little effect on the answers. The way to find the answer is by using the complementary event rule as P(2 people having the same birthday) = 1 - P(all have different birthdays). For example, suppose there were 3 people in the room. The probability that each had a different birthday would be \(\frac{365}{365} \cdot \frac{364}{365} \cdot \frac{363}{365}=\frac{365 P_{3}}{365^{3}}=0.992\) Hence, the probability that at least 2 of the 3 people will have the same birthday will be \(1-0.992=0.008\) Hence, for \(k\) people, the formula is P(at least 2 people have the same birthday) \(=1-\frac{365 P_{k}}{365^{k}}\) Using your calculator, complete the table and verify that for at least a 50% chance of 2 people having the same birthday, 23 or more people will be needed.

Problem 4CTC We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person? Explain your answer.

Health and Wellness Assume that the gender distribution of babies is such that one-half the time females are born and one-half the time males are born. In a family of 3 children, what is the probability that all are girls? In a family of 4? Is it unusual that in a family with 4 children all would be girls? In a family of 5?

Determine whether each statement is true or false. If the statement is false, explain why. If two events are dependent, they must have the same probability of occurring.

Politics and Economics Consider the U.S. Senate. Find out about the composition of any three of the Senate’s standing committees. How many different committees of Senators are possible, knowing the party composition of the Senate and the number of committee members from each party for each committee?

Problem 6CQ Determine whether each statement is true or false. If the statement is false, explain why An event and its complement can occur at the same time.

Your Class Research the famous Monty Hall probability problem. Conduct a simulation of the Monty Hall problem online using a simulation program or in class using live “contestants”. After 50 simulations compare your results to those stated in the research you did. Did your simulation support the conclusions?

Rolling Two Dice When two dice are rolled, find the probability of getting a. A sum of 5 or 6 b. A sum greater than 9 c. A sum less than 4 or greater than 9 d. A sum that is divisible by 4 e. A sum of 14 f. A sum less than 13

Determine whether each statement is true or false. If the statement is false, explain why. The arrangement ABC is the same as BAC for combinations.

Breakfast Drink In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred juice as her or his primary drink.

Problem 7RE Budget Rental Cars Cheap Rentals has nothing but budget cars for rental. The probability that a car has air conditioning is 0.5, and the probability that a car has a CD player is 0.37. The probability that a car has both air conditioning and a CD player is 0.06. What is the probability that a randomly selected car has neither air conditioning nor a CD player? (4–2)

Breakfast Drink In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred juice as her or his primary drink.

Select the best answer. The probability that an event happens is 0.42. What is the probability that the event won’t happen? a. 0.42 c. 0 b. 0.58 d. 1

Problem 9RE Car and Boat Ownership The probability that a person owns a car is 0.80, that a person owns a boat is 0.30, and that a person owns both a car and a boat is 0.12. Find the probability that a person owns either a boat or a car. (4–2)

Car Purchases There is a 0.39 probability that John will purchase a new car, a 0.73 probability that Mary will purchase a new car, and a 0.36 probability that both will purchase a new car. Find the probability that neither will purchase a new car.

Problem 10CQ Select the best answer. When a meteorologist says that there is a 30% chance of showers, what type of probability is the person using? a. Classical ________________ b. Empirical ________________ c. Relative ________________ d. Subjective

Problem 11RE Online Course Selection Roughly 1in 6 students enrolled in higher education took at least one online course last fall. Choose 5 enrolled students at random. Find the probability that a. All 5 took online courses b. None of the 5 took a course online c. At least 1 took an online course (4–2) Source: www.encarta.msn.com

Select the best answer. The sample space for tossing 3 coins consists of how many outcomes? a. 2 b. 4 c. 6 d. 8

Problem 12RE Purchasing Sweaters During a sale at a men’s store. 16 white sweaters, 3 red sweaters, 9 blue sweaters, and 7 yellow sweaters were purchased. If a customer is selected at random, find the probability that he bought. a. A?blue sweater ________________ b. A yellow or a white sweater ________________ c. A red, a blue, or a yellow sweater ________________ d. A sweater that was not white (4–2)

Problem 13CQ Select the best answer. When two dice are rolled, the sample space consists of how many events? a. 6 ________________ b. 12 ________________ c. 36 ________________ d. 54

Select the best answer. The complement of guessing 5 correct answers on a 5 -question true/false exam is a. Guessing 5 incorrect answers b. Guessing at least 1 incorrect answer c. Guessing at least 1 correct answer d. Guessing no incorrect answers

Select the best answer. What is nP0? a. 0 b. 1 c. n d. It cannot be determined.

Problem 13RE Drawing Cards Three cards are drawn from an ordinary deck without replacement. Find the probability of getting a. All black cards ________________ b. All spades ________________ c. All queens (4–3)

Problem 14RE Coin Toss and Card Drawn A coin is tossed and a card is drawn from a deck. Find the probability of getting a. A head and a 6 ________________ b. A tail and a red card ________________ c. A head and a club (4–3)

Problem 16CQ Select the best answer. What is 0!? a. 0 ________________ b. 1 ________________ c. Undefined ________________ d. 10

Problem 15RE Movie Releases The top five countries for movie releases so far this year are the United States with 471 releases. United Kingdom with 386, Japan with 79, Germany with 316, and France with 132. Choose 1 new release at random. Find the probability that it is a. European ________________ b. From the United States ________________ c. German or French ________________ d. German given that it is European (4–2) Source: www.showbizdata.com

Problem 15CQ Select the best answer. What is the number of permutations of 6 different objects taken all together? a. 0 ________________ b. 1 ________________ c. 36 ________________ d. 720

Select the best answer. What is nCn? a. 0 b. 1 c. n d. It cannot be determined.

Effectiveness of Vaccine A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a person is selected at random, find the probability that he or she will contract the disease.

Factory Output A manufacturing company has three factories: X, Y, and Z. The daily output of each is shown here. Product Factory X Factory Y Factory Z TVs 18 32 15 Stereos 6 20 13 If 1 item is selected at random, find these probabilities. a. It was manufactured at factory X or is a stereo. b. It was manufactured at factory Y or factory Z. c. It is a TV or was manufactured at factory Z.

Complete the following statements with the best answer. The set of all possible outcomes of a probability experiment is called the ___________.

Complete the following statements with the best answer. If an event cannot occur, its probability is ___________.

Problem 19CQ Complete the following statements with the best answer. The probability of an event can be any number between and including __________ and ________.

Problem 19RE Car Purchase The probability that Sue will live on campus and buy a new car is 0.37. If the probability that she will live on campus is 0.73, find the probability that she will buy a new car, given that she lives on campus. (4–3)

Complete the following statements with the best answer. The sum of the probabilities of the events in the sample space is ________.

Problem 20RE Applying Shipping Labels Four unmarked packages have lost their shipping labels, and you must reapply them. What is the probability that you apply the labels and get all 4 of them correct? Exactly 3 correct? Exactly 2? At least 1 correct? (4–3)

Problem 21RE Health Club Membership Of the members of the Blue River Health Club, 43% have a lifetime membership and exercise regularly (three or more times a week). If 75% of the club members exercise regularly, find the probability that a randomly selected member is a life member, given that he or she exercises regularly. (4–3)

Complete the following statements with the best answer. When two events cannot occur at the same time, they are said to be ________.

Problem 22RE Bad Weather The probability that it snows and the bus arrives late is 0.023. Jose hears the weather forecast, and there is a 40% chance of snow tomorrow. Find the probability that the bus will be late, given that it snows. (4–3)

When a card is drawn, find the probability of getting a. A jack b. A 4 c. A card less than 6 (an ace is considered above 6)

Selecting a Card When a card is drawn from a deck, find the probability of getting a. A diamond b. A 5 or a heart c. A 5 and a heart d. A king e. A red card

Education Level and Smoking At a large factory, the employees were surveyed and classified according to their level of education and whether they smoked. The data are shown in the table. Educational level Smoking habit Not high school graduate High school graduate College graduate Smoke 6 14 19 Do not smoke 18 7 25

Problem 24RE War Veterans Approximately 11% of the civilian population are veterans. Choose 5 civilians at random. What is the probability that none are veterans? What is the probability that at least 1 is a veteran? (4–3) Source: www.factfinder.census.gov

Problem 25CQ Selecting a Sweater At a men’s clothing store, 12 men purchased blue golf sweaters, 8 purchased green sweaters. 4 purchased gray sweaters, and 7 bought black sweaters. If a customer is selected at random, find the probability that he purchased a. A blue sweater ________________ b. A green or gray sweater ________________ c. A green or black or blue sweater ________________ d. A sweater that was not black

Problem 25RE DVD Players Eighty-one percent of U.S. households have DVD players. Choose 6 households at random. What is the probability that at least 1 does not have a DVD player? (4–3) Source: www.infoplease.com

Problem 26CQ Rolling Dice When 2 dice are rolled, find the probability of gening a. A sum of 6 or 7 ________________ b. A sum greater than 8 ________________ c. A sum less than 3 or greater than 8 ________________ d. A sum that is divisible by 3 ________________ e. A sum of 16 ________________ f. A sum less than 11

Problem 26RE Chronic Sinusitis The U.S. Department of Health and Human Services reports that 15% of Americans have chronic sinusitis. If 5 people are selected at random, find the probability that at least 1 has chronic sinusitis. (4–3) Source: 100% American.

Problem 27CQ Appliance Ownership The probability that a person owns a microwave oven is 0.75, that a person owns a compact disk player is 0.25, and that a person owns both a microwave and a CD player is 0.16. Find the probability that a person owns either a microwave or a CD player, but not both.

Starting Salaries Of the physics graduates of a university, 30% received a starting salary of $30,000 or more. If 5 of the graduates are selected at random, find the probability that all had a starting salary of $30,000 or more.

Problem 27RE Automobile License Plate An automobile license plate consists of 3 letters followed by 4 digits. How many different plates can be made if repetitions are allowed? If repetitions are not allowed? If repetitions are allowed in the letters but not in the digits? (4–4)

Problem 28RE Types of Copy Paper White copy paper is offered in 5 different strengths and 11 different degrees of brightness, recycled or not, and acid-free or not. How many different types of paper are available for order? (4–4)

Problem 30CQ Scholarships The probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35. If the probability that she is accepted by the college is 0.65, find the probability that she will obtain a scholarship given that she is accepted by the college.

Problem 32CQ Bowling and Club Membership Of the members of the Spring Lake Bowling Lanes, 57% have a lifetime membership and bowl regularly (three or more times a week). If 70% of the club members bowl regularly, find the probability that a randomly selected member is a lifetime member, given that he or she bowls regularly.

Problem 31CQ New Car Warranty The probability that a customer will buy a car and an extended warranty is 0.16. If the probability that a customer will purchase a car is 0.30, find the probability that the customer will also purchase the extended warranty.

Problem 29RE Baseball Players How many ways can 3 outfielders and 4 infielders be chosen from 5 outfielders and 7 infielders? (4–4)

Selecting Cards Five cards are drawn from an ordinary deck without replacement. Find the probability of getting a. All red cards b. All diamonds c. All aces

Committee Representation There are 6 Republican, 5 Democrat, and 4 Independent candidates. How many different ways can a committee of 3 Republicans, 2 Democrats, and 1 Independent be selected? (4–4)

Problem 33CQ Work and Weather The probability that Mike has to work overtime and it rains is 0.028. Mike hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given that it rains.

Song Selections A promotional MP3 player is available with the capacity to store 100 songs, which can be reordered at the push of a button. How many different arrangements of these songs are possible? (Note: Factorials get very big, very fast! How large a factorial will your calculator calculate?)

Problem 35CQ Heart Attacks In a certain high-risk group, the chances of a person having suffered a heart attack are 55%. If 6 people are chosen, find the probability that at least 1 will have had a heart attack.

Education of Factory Employees At a large factory, the employees were surveyed and classified according to their level of education and whether they attend a sports event at least once a month. The data are shown in the table. If an employee is selected at random, find the probability that a. The employee attends sports events regularly, given that he or she graduated from college (2- or 4-year degree) b. Given that the employee is a high school graduate, he or she does not attend sports events regularly

Rolling a Die A single die is rolled 4 times. Find the probability of getting at least one 5.

Problem 35RE Course Enrollment There are 12 students who wish to enroll in a particular course. There are only 4 seats left in the classroom. How many different ways can 4 students be selected to attend the class? (4–4)

Problem 34RE Employee Health Care Plans A new employee has a choice of 5 health care plans. 3 retirement plans, and 2 different expense accounts. If a person selects 1 of each option, how many different options does he or she have? (4–4)

Problem 36RE Candy Selection A candy store allows customers to select 3 different candies to be packaged and mailed. If there are 13 varieties available, how many possible selections can be made? (4–4)

Problem 37CQ Eye ColorIf 85% of all people have brown eyes and 6 people are selected at random, find the probability that at least 1 of them has brown eyes.

Problem 38CQ Singer Selection How many ways can 5 sopranos and 4 altos be selected from 7 sopranos and 9 altos?

Problem 39RE Book Selection If a student can select 5 novels from a reading list of 20 for a course in literature, how many different possible ways can this selection be done? (4–4)

Problem 39CQ Speaker Selection How many different ways can 8 speakers be seated on a stage?

Course Selection If a student can select one of 3 language courses, one of 5 mathematics courses and one of 4 history courses, how many different schedules can be made?

ID Cards One company’s ID cards consist of 5 letters followed by 2 digits. How many cards can be made if repetitions are allowed? If repetitions are not allowed?

Problem 40CQ Stocking Machines A soda machine servicer must restock and collect money from 15 machines, each one at a different location. How many ways can she select 4 machines to service in 1 day?

License Plates License plates are to be issued with 3 letters followed by 4 single digits. How many such license plates are possible? If the plates are issued at random, what is the probability that the license plate says USA followed by a number that is divisible by 5? (4–5)

How many different arrangements of the letters in the word number can be made?

Problem 43CQ Physics Test A physics test consists of 25 true/false questions. How many different possible answer keys can be made?

Territorial Selection Several territories and colonies today are still under the jurisdiction of another country France holds the most with 16 territories, the United Kingdom has 15, the United States has 14, and several other countries have territories as well. Choose 3 territories at random from those held by France, the United Kingdom, and the United States. What is the probability that all 3 belong to the same country? (4–5) Source: www.infoplease.com

Yahtzee Yahtzee is a game played with 5 dice. Players attempt to score points by rolling various combinations. When all 5 dice show the same number, it is called a Yahtee and scores 50 points for the first one and 100 points for each subsequent Yahtzee in the same game. What is the probability that a person throws a Yahtzee on the very first roll? What is the probability that a person throws two Yahtzees on two successive turns? (4–5)

Problem 45CQ Fruit Selection On a lunch counter, there are 3 oranges. 5 apples, and 2 bananas. If 3 pieces of fruit are selected, find the probability that 1 orange, 1 apple, and 1 banana are selected.

Problem 45RE Personnel Classification For a survey, a subject can be classified as follows: Gender, male or female Marital status: single, married, widowed, divorced Occupation: administration, faculty, staff Draw a tree diagram for the different ways a person can be classified. (4–4)

Problem 44CQ Cellular Telephones How many different ways can 5 cellular telephones be selected from 8 cellular phones?

Problem 46CQ Cruise Ship Activities A cruise director schedules 4 different movies, 2 bridge games, and 3 tennis games for a two-day period. If a couple selects 3 activities, find the probability that they attend 2 movies and 1 tennis game.

Problem 47CQ Committee Selection At a sorority meeting, there are 6 seniors. 4 juniors, and 2 sophomores. If a committee of 3 is to be formed, find the probability that 1 of each will be selected.

Problem 48CQ Banquet Meal Choices For a banquet, a committee can select beef, pork, chicken, or veal; baked potatoes or mashed potatoes: and peas or green beans for a vegetable. Draw a tree diagram for all possible choices of a meat, a potato, and a vegetable.