Solved: How many possible variations are there in Mozart’s

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

Problem 1TE How many phrases did Mozart write to create the Musical Dice Game minuet? Explain.

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 2TE How many possible variations are there in Mozart’s Musical Dice Game minuet? Explain.

Problem 3CQ 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 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 3TE Use technology to randomly select a number from 1 to 11 (a) What is the theoretical probability of each number from 1 to 11 occurring? ________________ (b) Use this procedure to select 100 integers from 1 to 11. Tally your results and compare them with the probabilities in part (a).

Problem 4CQ 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 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 4TE What is the probability of randomly selecting option 6, 7, or 8 for the first bar? For all 14 bars? Find each probability using (a) theoretical probability and (b) the results of Exercise 3(b). Use technology to randomly select a number from 1 to 11 (a) What is the theoretical probability of each number from 1 to 11 occurring? ________________ (b) Use this procedure to select 100 integers from 1 to 11. Tally your results and compare them with the probabilities in part (a). Exercise 3 Use technology to randomly select a number from 1 to 11 (b) Use this procedure to select 100 integers from 1 to 11. Tally your results and compare them with the probabilities in part (a).

Problem 5CQ In Exercise, find the probability of the vending company receiving (a) no defective units. ________________ (b) all defective units. ________________ (c) at least one good unit. 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 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 5TE Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total. (a) What is the theoretical probability of each total from 1 to 11? ________________ (b) Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a).

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 6TE Repeat Exercise 1 using the results of Exercise 2. Exercise 1 What is the probability of randomly selecting option 6, 7, or 8 for the first bar? For all 14 bars? Find each probability using (a) theoretical probability and (b) the results of Exercise 3(b). Exercise 2 Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total. (a) What is the theoretical probability of each total from 1 to 11? ________________ (b) Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a). Exercise 3 Use technology to randomly select a number from 1 to 11 (b) Use this procedure to select 100 integers from 1 to 11. Tally your results and compare them with the probabilities in part (a).

Problem 7CQ 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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.

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 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.

Problem 35E In Exercise, 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) Students in Public Charter Schools Find the probability of randomly selecting a school with 500 or more students.

Problem 36E In Exercise, 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) Students in Public Charter Schools Find the probability of randomly selecting a school with between 300 and 999 students, inclusive.

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

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

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

Problem 44E Exercises 44, perform the indicated calculation.

Problem 47E In Exercise, use combinations and permutations. Fifteen cyclists enter a race. How many ways can the cyclists finish first, second, and third?

Problem 48E 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 49E 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 50E 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 51E 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 52E 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 53E 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 54E 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 55E 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?