Chapter 5

Some people are in favor of reducing federal taxes to increase consumer spending and others are against it. Two persons are selected and their opinions are recorded. Assuming no one is undecided, list the possible outcomes.

A quality control inspector selects a part to be tested. The part is then declared acceptable, repairable, or scrapped. Then another part is tested. List the possible outcomes of this experiment regarding two parts.

A large company that must hire a new president prepares a final list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. a. \(2 / 5\) or.4 b. Classical a. What is the probability one of the minority candidates is hired? b. Which concept of probability did you use to make this estimate?

In each of the following cases, indicate whether classical, empirical, or subjective probability is used. a. A baseball player gets a hit in 30 out of 100 times at bat. The probability is .3 that he gets a hit in his next at bat. b. A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is chosen as the spokesperson? c. You purchase one of 5 million tickets sold for Lotto Canada. What is the likelihood you win the \(\$ 1\) million jackpot? d. The probability of an earthquake in northern California in the next 10 years is . 80 .

A firm will promote two employees out of a group of six men and three women. a. List the outcomes of this experiment if there is particular concern about gender equity. b. Which concept of probability would you use to estimate these probabilities?

A sample of 40 oil industry executives was selected to test a questionnaire. One question about environmental issues required a yes or no answer. a. What is the experiment? b. List one possible event. c. Ten of the 40 executives responded yes. Based on these sample responses, what is the probability that an oil industry executive will respond yes? d. What concept of probability does this illustrate? e. Are each of the possible outcomes equally likely and mutually exclusive?

Bank of America customers select their own three-digit personal identification number (PIN) for use at ATMs. a. Think of this as an experiment and list four possible outcomes. b. What is the probability Mr. Jones and Mrs. Smith select the same PIN? c. Which concept of probability did you use to answer (b)?

The events \(A\) and \(B\) are mutually exclusive. Suppose \(P(A)=.30\) and \(P(B)=.20 .\) What is the probability of either \(A\) or \(B\) occurring? What is the probability that neither \(A\) nor \(B\) will happen?

The events \(X\) and \(Y\) are mutually exclusive. Suppose \(P(X)=.05\) and \(P(Y)=.02 .\) What is the probability of either \(X\) or \(Y\) occurring? What is the probability that neither \(X\) nor \(Y\) will happen?

The chair of the board of directors says, "There is a 50 percent chance this company will earn a profit, a 30 percent chance it will break even, and a 20 percent chance it will lose money next quarter." a. Use an addition rule to find the probability the company will not lose money next quarter. b. Use the complement rule to find the probability it will not lose money next quarter.

Suppose the probability you will get an \(\mathrm{A}\) in this class is .25 and the probability you will get a \(\mathrm{B}\) is \(.50 .\) What is the probability your grade will be above a \(C ?\)

Two coins are tossed. If \(A\) is the event "two heads" and \(B\) is the event "two tails," are \(A\) and \(B\) mutually exclusive? Are they complements?

The probabilities of the events \(A\) and \(B\) are .20 and .30 , respectively. The probability that both \(A\) and \(B\) occur is .15. What is the probability of either \(A\) or \(B\) occurring?

Let \(P(X)=.55\) and \(P(Y)=.35 .\) Assume the probability that they both occur is .20. What is the probability of either \(X\) or \(Y\) occurring?

Suppose the two events \(A\) and \(B\) are mutually exclusive. What is the probability of their joint occurrence?

A student is taking two courses, history and math. The probability the student will pass the history course is \(.60,\) and the probability of passing the math course is \(.70 .\) The probability of passing both is .50. What is the probability of passing at least one?

A survey of grocery stores in the Southeast revealed 40 percent had a pharmacy, 50 percent had a floral shop, and 70 percent had a deli. Suppose 10 percent of the stores have all three departments, 30 percent have both a pharmacy and a deli, 25 percent have both \(a\) floral shop and deli, and 20 percent have both a pharmacy and floral shop. a. What is the probability of selecting a store at random and finding it has both a pharmacy and a floral shop? b. What is the probability of selecting a store at random and finding it has both a pharmacy and a deli? c. Are the events "select a store with a deli" and "select a store with a pharmacy" mutually exclusive? d. What is the name given to the event of "selecting a store with a pharmacy, a floral shop, and a deli?" e. What is the probability of selecting a store that does not have all three departments?

A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both. a. What is the probability a vacationer will visit at least one of these attractions? b. What is the probability .35 called? c. Are the events mutually exclusive? Explain.

Suppose \(P(A)=.40\) and \(P(B / A)=.30 .\) What is the joint probability of \(A\) and \(B ?\)

A local bank reports that 80 percent of its customers maintain a checking account, 60 percent have a savings account, and 50 percent have both. If a customer is chosen at random, what is the probability the customer has either a checking or a savings account? What is the probability the customer does not have either a checking or a savings account?

All Seasons Plumbing has two service trucks that frequently break down. If the probability the first truck is available is .75, the probability the second truck is available is . \(50,\) and the probability that both trucks are available is .30, what is the probability neither truck is available?

Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones. a. What is the probability the first two electric toothbrushes sold will be returned to the drugstore because they are defective? b. What is the probability the first two electric toothbrushes sold will not be defective?

An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value, (2) decreasing in value, or (3) remaining the same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.

The board of directors of a small company consists of five people. Three of those are "strong leaders." If they buy an idea, the entire board will agree. The other "weak" members have no influence. Three salespeople are scheduled, one after the other, to make sales presentations to a board member of the salesperson's choice. The salespeople are convincing but do not know who the "strong leaders" are. However, they will know who the previous salespeople spoke to. The first salesperson to find a strong leader will win the account. Do the three salespeople have the same chance of winning the account? If not, find their respective probabilities of winning.

If you ask three strangers about their birthdays, what is the probability: (a) All were born on Wednesday? (b) All were born on different days of the week? (c) None were born on Saturday?

Solve the following: a. \(40 ! / 35 !\) b. \({ }_{7} P_{4}\) c. \({ }_{5} C_{2}\)

Solve the following: a. 20!/17! b. \({ }_{9} P_{3}\) c. \({ }_{7} C_{2}\)

There are 10 members on the Community Appearance Board of Los Angeles County. This board is charged with ensuring that all new construction projects meet county appearance standards. A new terminal is to be added to the Los Angeles International Airport. A subcommittee of four members is to be created to review the initial drawing of the project. How many different subcommittees are possible?

A telephone number consists of seven digits, the first three representing the exchange. How many different telephone numbers are possible within the 537 exchange?

An overnight express company must include five cities on its route. How many different routes are possible, assuming that it does not matter in which order the cities are included in the routing?

A representative of the Environmental Protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?

USA Today/Gallup Polls developed 15 questions designed to rate the performance of the president of the United States. They will select 10 of these questions. How many different arrangements are there for the order of the 10 selected questions?

A company is creating three new divisions and seven managers are eligible to be appointed head of a division. How many different ways could the three new heads be appointed?

The number of times a particular event occurred in the past is divided by the number of occurrences. What is this approach to probability called?

The probability that the cause and the cure for all cancers will be discovered before the year 2010 is . 20 . What viewpoint of probability does this statement illustrate?

Define each of these items: a. Conditional probability b. Event c. Joint probability

The first card selected from a standard 52 -card deck is a king. a. If it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. If the king is not replaced, what is the probability that a king will be drawn on the second selection? c. What is the probability that a king will be selected on the first draw from the deck and another king on the second draw (assuming that the first king was not replaced)?

Armco, a manufacturer of traffic light systems, found that under accelerated- life tests, 95 percent of the newly developed systems lasted 3 years before failing to change signals properly. a. If a city purchased four of these systems, what is the probability all four systems would operate properly for at least 3 years? b. Which rule of probability does this illustrate? c. Using letters to represent the four systems, write an equation to show how you arrived at the answer to part (a).

In a management trainee program at Claremont Enterprises, 80 percent of the trainees are female and 20 percent male. Ninety percent of the females attended college, and 78 percent of the males attended college. a. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college? b. Are gender and attending college independent? Why? c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities. d. Do the joint probabilities total 1.00 ? Why?

Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is .90. We select four flights from yesterday for study. a. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time? b. What is the likelihood that none of the selected flights arrived within 15 minutes of the scheduled time? c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time?

There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are production workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose an employee is selected: a. What is the probability the selected employee is a production worker? b. What is the probability the selected employee is either a production worker or a supervisor? c. Refer to part (b). Are these events mutually exclusive? d. What is the probability the selected employee is neither a production worker nor a supervisor?

Joe Mauer of the Minnesota Twins had the highest batting average in the 2006 Major League Baseball season. His average was . \(347 .\) So assume the probability of getting a hit is . 347 for each time he batted. In a particular game assume he batted three times. a. This is an example of what type of probability? b. What is the probability of getting three hits in a particular game? c. What is the probability of not getting any hits in a game? d. What is the probability of getting at least one hit?

The probability that a cruise missile hits its target on any particular mission is .80. Four cruise missiles are sent after the same target. What is the probability: a. They all hit the target? b. None hit the target? c. At least one hits the target?

Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at the graduation. a. What is the probability both of the selected students plan to attend college? b. What is the probability one of the two selected students plans to attend college?

Brooks Insurance, Inc., wishes to offer life insurance to men age 60 via the Internet. Mortality tables indicate the likelihood of a 60-year-old man surviving another year is .98. If the policy is offered to five men age 60 : a. What is the probability all five men survive the year? b. What is the probability at least one does not survive?

Refer to Exercise \(56,\) but assume there are 10 homes in the Quail Creek area and four of them have a security system. Three homes are selected at random: a. What is the probability all three of the selected homes have a security system? b. What is the probability none of the three selected homes have a security system? c. What is the probability at least one of the selected homes has a security system? d. Did you assume the events to be dependent or independent?

There are 20 families living in the Willbrook Farms Development. Of these families 10 prepared their own federal income taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 3 by H\&R Block. a. What is the probability of selecting a family that prepared their own taxes? b. What is the probability of selecting two families both of which prepared their own taxes? c. What is the probability of selecting three families, all of which prepared their own taxes? d. What is the probability of selecting two families, neither of which had their taxes prepared by H\&R Block?

The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom are women. A new policy and procedures manual is to be written for the company. A committee of 3 is randomly selected from the board to do the writing. a. What is the probability that all members of the committee are men? b. What is the probability that at least 1 member of the committee is a woman?

Althoff and Roll, an investment firm in Augusta, Georgia, advertises extensively in the Augusta Morning Gazette, the newspaper serving the region. The Gazette marketing staff estimates that 60 percent of Althoff and Roll's potential market read the newspaper. It is further estimated that 85 percent of those who read the Gazette remember the Althoff and Roll advertisement a. What percent of the investment firm's potential market sees and remembers the advertisement? b. What percent of the investment firm's potential market sees, but does not remember the advertisement?

An Internet company located in Southern California has season tickets to the Los Angeles Lakers basketbal games. The company president always invites one of the four vice presidents to attend games with him, and claims he selects the person to attend at random. One of the four vice presidents has not been invited to attend any of the last five Lakers home games. What is the likelihood this could be due to chance?