Determine whether the events are mutually exclusive.

Problem 53E In Exercise, use counting principles to find the probability. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the probability of choosing (a) four men? ________________ (b) four women? ________________ (c) two men and two women? ________________ (d) one man and three women?

Problem 1CQ The access code for a warehouse’s security system consists of six digits. The first digit cannot be 0 and the last digit must be even. How many access codes are possible?

Problem 1CT Take this test as you would take a test in class. Thirty runners compete in a cross-country race. Your school has five runners in the race. What is the probability that three runners from your school place first, second, and third?

Problem 2E In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate. Experiment: Rolling 2 six-sided dice Event: Getting a sum of 4 or 5

Problem 1E In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate. Experiment: Tossing four coins Event: Getting three heads

The table shows the number (in thousands) of earned degrees, by level and gender, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics) A person who earned a degree in the year is randomly selected. Find the probability of selecting someone who (a) earned a bachelor’s degree. (b) earned a bachelor’s degree, given that the person is a female. (c) earned a bachelor’s degree, given that the person is not a female. (d) earned an associate’s degree or a bachelor’s degree. (e) earned a doctorate, given that the person is a female. (f) earned a master’s degree or is a male. (g) earned an associate’s degree and is a male. (h) is a female, given that the person earned a bachelor’s degree.

Problem 3CQ Which event(s) in Exercise 2 can be considered unusual? Explain your reasoning. Exercise 2 The table shows the number (in thousands) of earned degrees, by level and gender, conferred in the United States in a recent year. (Source: U.S. National Center for Education Statistics) Gender Male Female Total Level of degree Associate’s 361 581 942 Bachelor’s 734 982 1716 Master’s 292 439 731 Doctoral 80 84 164 Total 1467 2086 3553 A person who earned a degree in the year is randomly selected. Find the probability of selecting someone who (a) earned a bachelor’s degree. ________________ (b) earned a bachelor’s degree, given that the person is a female. ________________ (c) earned a bachelor’s degree, given that the person is not a female. ________________ (d) earned an associate’s degree or a bachelor’s degree. ________________ (e) earned a doctorate, given that the person is a female. ________________ (f) earned a master’s degree or is a male. ________________ (g) earned an associate’s degree and is a male. ________________ (h) is a female, given that the person earned a bachelor’s degree.

Problem 3E In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate. Experiment: Choosing a month of the year Event: Choosing a month that begins with the letter J

Problem 3CT Determine whether the events are mutually exclusive. Explain your reasoning. Event A: Randomly select a student born on the 30th of a month Event B: Randomly select a student with a birthday in February

Problem 4CQ Determine whether the events are mutually exclusive. Then determine whether the events are independent or dependent. Explain your reasoning. Event A: A golfer scoring the best round in a four-round tournament Event B: Losing the golf tournament

Problem 4CT The table shows the results of a survey in which 28,295 adults were asked whether they had a cold or the flu on the previous day. (Adapted from Gallup) Colds Flu Neither Total Smoker 526 153 4,980 5,659 Nonsmoker 1,494 430 20,712 22,636 Total 2,020 583 25,692 28,295 A person is selected at random from the sample. Find the probability of each event. (a) The person had a cold (b) The person had a cold or the flu (c) The person had neither illness, given that the person is a smoker (d) The person had neither illness, given that the person is a nonsmoker (e) The person is a smoker, given that the person had the flu (f) The person had the flu or is a nonsmoker (g) The person had a cold and is a smoker

Problem 4E In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate. Experiment: Guessing the gender(s) of the three children in a family Event: The family has two boys

Problem 5CQ From a pool of 30 candidates, the offices of president, vice president, secretary, and treasurer will be filled. In how many different ways can the offices be filled?

Problem 6CQ A shipment of 250 netbooks contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive (a) no defective units. ________________ (b) all defective units. ________________ (c) at least one good unit.

Problem 5CT Which event(s) in Exercise 4 can be considered unusual? Explain your reasoning. The table shows the results of a survey in which 28,295 adults were asked whether they had a cold or the flu on the previous day. (Adapted from Gallup) Colds Flu Neither Total Smoker 526 153 4,980 5,659 Nonsmoker 1,494 430 20,712 22,636 Total 2,020 583 25,692 28,295 A person is selected at random from the sample. Find the probability of each event. (a) The person had a cold (b) The person had a cold or the flu (c) The person had neither illness, given that the person is a smoker (d) The person had neither illness, given that the person is a nonsmoker (e) The person is a smoker, given that the person had the flu (f) The person had the flu or is a nonsmoker (g) The person had a cold and is a smoker

Problem 5E In Exercise, use the Fundamental Counting Principle. A student must choose from 7 classes to take at 8:00 a.m., 4 classes to take at 9:00 a.m., and 3 classes to take at 10:00 a.m. How many ways can the student arrange the schedule?

Problem 7CQ In Exercise, find the probability of the vending company receiving (a) no defective units. ________________ (b) all defective units. ________________ (c) at least one good unit. Reference Exercise A shipment of 250 netbooks contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive (a) no defective units. (b) all defective units. (c) at least one good unit.

Problem 7CT There are 16 students giving final presentations in your history course. (a) Three students present per day. How many presentation orders are possible for the first day? ________________ (b) Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on the same unit are indistinguishable from each other?

Problem 6E In Exercise, use the Fundamental Counting Principle. The state of Virginia’s license plates have three letters followed by four digits. Assuming that any letter or digit can be used, how many different license plates are possible?

Problem 6CT A person is selected at random from the sample in Exercise 4. Are the events “the person had a cold” and “the person is a smoker” independent or dependent? Explain your reasoning.

Problem 7E In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. On the basis of prior counts, a quality control officer says there is a 0.05 probability that a randomly chosen part is defective.

Problem 12E In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The chance that a randomly selected person in the United States is between 15 and 29 years old is about 21%. (Source: U.S. Census Bureau)

Problem 10E In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability that a person can roll his or her tongue is 70%.

Problem 8E In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability of randomly selecting five cards of the same suit from a standard deck of 52 playing cards is about 0.002.

Problem 11E In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability of rolling 2 six-sided dice and getting a sum greater than 9 is ?.

Problem 9E In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The chance that Corporation A’s stock price will fall today is 75%.

Problem 13E In Exercise, use the table, which shows the approximate distribution of the sizes of firms for a recent year. (Source: Adapted from U.S. Small Business Administration) Number of employees 1 to 4 5 to 9 10 to 19 20 to 99 100 or more Percent of firms 42.9% 15.1% 9.6% 10.0% 22.4% Find the probability that a randomly selected firm will have at least 10 employees.

Problem 14E In Exercise, use the table, which shows the approximate distribution of the sizes of firms for a recent year. (Source: Adapted from U.S. Small Business Administration) Number of employees 1 to 4 5 to 9 10 to 19 20 to 99 100 or more Percent of firms 42.9% 15.1% 9.6% 10.0% 22.4% Find the probability that a randomly selected firm will have fewer than 20 employees.

Problem 15E Telephone Numbers In Exercise, use the following information. The telephone numbers for a region of a state have an area code of 570. The next seven digits represent the local telephone numbers for that region. A local telephone number cannot begin with a 0 or 1. Your cousin lives within the given area code. What is the probability of randomly generating your cousin’s telephone number on the first try?

Problem 17E In Exercise, use the table, which shows the number of students who took the July 2012 California Bar Examination for the first time and the number of students who repeated the exam. (Source: The State Bar of California) Passed Failed Total First time 4427 2058 6485 Repeat 407 1845 2252 Total 4834 3903 8737 Find the probability that a student failed, given that the student took the exam for the first time.

Problem 19E In Exercise, determine whether the events are independent or dependent. Explain your reasoning. Tossing a coin four times, getting four heads, and tossing it a fifth time and getting a head

Problem 16E Telephone Numbers In Exercise, use the following information. The telephone numbers for a region of a state have an area code of 570. The next seven digits represent the local telephone numbers for that region. A local telephone number cannot begin with a 0 or 1. Your cousin lives within the given area code. What is the probability of not randomly generating your cousin’s telephone number on the first try?

Problem 18E In Exercise, use the table, which shows the number of students who took the July 2012 California Bar Examination for the first time and the number of students who repeated the exam. (Source: The State Bar of California) Passed Failed Total First time 4427 2058 6485 Repeat 407 1845 2252 Total 4834 3903 8737 Find the probability that a student repeated the exam, given that the student passed.

Problem 20E In Exercise, determine whether the events are independent or dependent. Explain your reasoning. Taking a driver’s education course and passing the driver’s license exam

Problem 21E In Exercise, determine whether the events are independent or dependent. Explain your reasoning. Getting high grades and being awarded an academic scholarship

Problem 22E You are given that P(A) = 0.35 and P(B) = 0.25. Do you have enough information to find P(A and B)? Explain.

Problem 26E In Exercise, determine whether the events are mutually exclusive. Explain your reasoning. Event A: Randomly select a person who loves cats. Event B: Randomly select a person who owns a dog.

Problem 28E You are given that P(A) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B) ? Explain.

Problem 29E A random sample of 250 working adults found that 74% access the Internet at work, 88% access the Internet at home, and 72% access the Internet at both work and home. Find the probability that a person in this sample selected at random accesses the Internet at home or at work.

Problem 30E A sample of automobile dealerships found that 19% of automobiles sold are silver, 22% of automobiles sold are sport utility vehicles (SUVs), and 16% of automobiles sold are silver SUVs. Find the probability that a randomly chosen sold automobile from this sample is silver or an SUV.

Problem 27E In Exercise, determine whether the events are mutually exclusive. Explain your reasoning. Event A: Randomly select a U.S. adult registered to vote in Illinois. Event B: Randomly select a U.S. adult registered to vote in Florida.

Problem 31E In Exercise, find the probability. A card is randomly selected from a standard deck of 52 playing cards. Find the probability that the card is between 4 and 8, inclusive, or is a club.

Problem 33E In Exercise, find the probability. A 12-sided die, numbered 1 to 12, is rolled. Find the probability that the roll results in an odd number or a number less than 4.

Problem 32E In Exercise, find the probability. A card is randomly selected from a standard deck of 52 playing cards. Find the probability that the card is red or a queen.

In Exercises 35 and 36, use the pie chart, which shows the percent distribution of the number of students in U.S. public charter schools. (Source: U.S. National Center for Education Statistics) Find the probability of randomly selecting a school with 500 or more students.

Problem 34E In Exercise, find the probability. An 8-sided die, numbered 1 to 8, is rolled. Find the probability that the roll results in an even number or a number greater than 6.

In Exercises 35 and 36, use the pie chart, which shows the percent distribution of the number of students in U.S. public charter schools. (Source: U.S. National Center for Education Statistics) Find the probability of randomly selecting a school with between 300 and 999 students, inclusive.

In Exercises 37–40, use the Pareto chart, which shows the results of a survey in which 326,000 adults were asked which religion they identify with. (Adapted from Gallup) Find the probability of randomly selecting an adult who identifies as Catholic or Muslim.

In Exercises 37–40, use the Pareto chart, which shows the results of a survey in which 326,000 adults were asked which religion they identify with. (Adapted from Gallup) Find the probability of randomly selecting an adult who has no religious identity or gives no response.

In Exercises 37–40, use the Pareto chart, which shows the results of a survey in which 326,000 adults were asked which religion they identify with. (Adapted from Gallup) Find the probability of randomly selecting an adult who does not identify as Protestant/Other Christian.

Problem 41E Exercises 41, perform the indicated calculation. 11P2

Problem 42E Exercises 42, perform the indicated calculation. 8P6

In Exercises 37–40, use the Pareto chart, which shows the results of a survey in which 326,000 adults were asked which religion they identify with. (Adapted from Gallup) Find the probability of randomly selecting an adult who does not identify as Jewish or Mormon.

Problem 43E Exercises 43, perform the indicated calculation. 7C4

Problem 45E In Exercise, use combinations and permutations. Fifteen cyclists enter a race. How many ways can the cyclists finish first, second, and third?

In Exercises 41– 44, perform the indicated calculation. \(\frac{{ }_{5} C_{3}}{{ }_{10} C_{3}}\) ________________ Equation Transcription: Text Transcription: frac{_{5}C_3}{_{10}C_3}

Problem 46E In Exercise, use combinations and permutations. Five players on a basketball team must each choose a player on the opposing team to defend. In how many ways can the players choose their defensive assignments?

Problem 47E In Exercise, use combinations and permutations. A literary magazine editor must choose 4 short stories for this month’s issue from 17 submissions. In how many ways can the editor choose this month’s stories?

Problem 48E In Exercise, use combinations and permutations. An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the 2 people?

Problem 49E In Exercise, use counting principles to find the probability. A full house consists of three of one kind and two of another kind. You are dealt a hand of five cards from a standard deck of 52 playing cards. Find the probability of being dealt a full house consisting of three kings and two queens.

Problem 50E In Exercise, use counting principles to find the probability. A security code consists of three letters followed by one digit. The first letter cannot be A, B, or C. What is the probability of guessing the security code on the first try?

Problem 51E In Exercise, use counting principles to find the probability. A batch of 200 calculators contains 3 defective units. What is the probability that a sample of three calculators will have (a) no defective calculators? ________________ (b) all defective calculators? ________________ (c) at least one defective calculator? ________________ (d) at least one nondefective calculator?

Problem 52E In Exercise, use counting principles to find the probability. A batch of 350 raffle tickets contains four winning tickets. You buy four tickets. What is the probability that you have (a) no winning tickets? ________________ (b) all of the winning tickets? ________________ (c) two winning tickets? ________________ (d) at least one winning ticket?

Problem 23E In Exercise, find the probability of the sequence of events. You are shopping, and your roommate has asked you to pick up toothpaste and dental rinse. However, your roommate did not tell you which brands to get. The store has eight brands of toothpaste and five brands of dental rinse. What is the probability that you will purchase the correct brands of both products? Is this an unusual event? Explain.

Problem 24E In Exercise 24, find the probability of the sequence of events. Your sock drawer has 18 folded pairs of socks, with 8 pairs of white, 6 pairs of black, and 4 pairs of blue. What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair? Is this an unusual event? Explain.

Problem 25E In Exercise, determine whether the events are mutually exclusive. Explain your reasoning. Event A: Randomly select a red jelly bean from a jar. Event B: Randomly select a yellow jelly bean from the same jar.

Problem 2CT A security code consists of a person’s first and last initials followed by four digits. (a) What is the probability of guessing a person’s security code on the first try? ________________ (b) What is the probability of not guessing a person’s security code on the first try? ________________ (c) You know a person’s first name and that the last digit is odd. What is the probability of guessing this person’s security code on the first try? ________________ (d) Are the statements in parts (a)-(c) examples of classical probability, empirical probability, or subjective probability? Explain your reasoning.