Chapter 5 Assignment

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. Assume no one is undecided. Find the number of possible outcomes.

4

The marketing research department at PepsiCo plans a national survey of 2,500 teenagers regarding a newly developed soft drink. Each teenager will be asked to compare it with his or her favorite soft drink. What is the experiment?

Asking teenagers their reactions to the newly developed soft drink.

An overnight express company must include eight cities on its route. How many different routes are possible, assuming that it does matter in which order the cities are included in the routing?

Number of different routes: 40,320

All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is 0.79, the probability the second truck is available is 0.56, and the probability that both trucks are available is 0.43, what is the probability neither truck is available?

Probability: 0.09

A student is taking two courses, history and math. The probability the student will pass the history course is 0.52, and the probability of passing the math course is 0.64. The probability of passing both is 0.42. What is the probability of passing at least one?

Probability: 0.74

Two components, A and B, operate in series. Being in series means that for the system to operate, both components A and B must work. Assume the two components are independent. The probability A works is 0.90 and the probability B functions is also 0.90. What is the probability the system works under these conditions?

Probability: 0.80

A company uses three backup servers to secure its data. The probability that a server fails is 0.15. Assuming that the failure of a server is independent of the other servers, what is the probability that one or more of the servers is operational?

Probability: 0.996625

The events X and Y are mutually exclusive. Suppose P(X)=0.07 and P(Y)=0.05. What is the probability of either X or Y occurring? b. What is the probability that neither X nor Y will happen?

a. 0.12 b. 0.88

A study of 208 advertising firms revealed their income after taxes: Income after Taxes Number of Firms Under $1 million 92 $1 million to $20 million 53 $20 million or more 63 a. What is the probability an advertising firm selected at random has under $1 million in income after taxes? b. What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more?

a. 0.44 b. 0.56

The events A and B are mutually exclusive. Suppose P(A)=0.23 and P(B)=0.26. a. What is the probability of either A or B occuring? b. What is the probability that neither A nor B will happen?

a. 0.49 b. 0.51

Refer to the following table. a. Determine P(B2) b. Determine P(A3/B1) c. Determine P(A1 and B1)

a. 0.62 b. 0.44 c. 0.04

Solve the following: a. 21!/17! b. 7P4 c. 10C6

a. 143,640 b. 840 c. 210

A sample of 47 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. Which of the following are possible events. c. 22 of the 47 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?

a. 47 b. 11 people respond "Yes." 36 people respond "Yes." 33 people respond "No." The questionnaire fails to reach one executive. c. Probability: 0.47 d. Empirical e. The outcomes are equally likely and are also mutually exclusive.

In each of the following cases, indicate whether classical, empirical, or subjective probability is used. a. A baseball player gets a hit in 40 out of 122 times at bat. The probability is 0.33 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 eight is randomly chosen as the spokesperson? c. You purchase a ticket for the Lotto Canada lottery. Over fourteen million tickets were sold. What is the likelihood you will win the $4 million jackpot? d. The probability of an earthquake in northern California in the next 13 years above 14.0 on the Richter Scale is 0.85.

a. Empirical b. Classical c. Classical d. Empirical

A case of 24 cans contains one can that is contaminated. Three cans are to be chosen randomly for testing. a. How many different combinations of three cans could be selected? b. What is the probability that the contaminated can is selected for testing? (Round your answer to 3 decimal places.)

a. Number of different combinations: 2,024 b. Probability: 0.125

A survey of 46 students at the Wall College of Business showed the following majors: Accounting: 12 Finance: 6 Economics: 6 Management: 10 Marketing: 12 From the 46 students, suppose you randomly select a student. a. What is the probability he or she is a management major? b. Which concept of probability did you use to make this estimate?

a. Probability: 0.217 b. Empirical

A survey of 545 college students asked: What is your favorite winter sport? And, what type of college do you attend? The results are summarized below: Using these 545 students as the sample, a student from this study is randomly selected. a. What is the probability of selecting a student whose favorite sport is skiing? b. What is the probability of selecting a junior-college student? c. If the student selected is a four-year-college student, what is the probability that the student prefers ice skating? d. If the student selected prefers snowboarding, what is the probability that the student is in junior college? e. If a graduate student is selected, what is the probability that the student prefers skiing or ice skating?

a. Probability: 0.3138 b. Probability: 0.2844 c. Probability: 0.3333 d. Probability: 0.3223 e. Probability: 0.6722

A recent survey reported in Bloomberg Businessweek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money. If a company is randomly selected from the list of 28 studied, what is the probability: a. The CEO made more than $1 million? b. The CEO made more than $1 million or the shareholders lost money? c. The CEO made more than $1 million given the shareholders lost money? d. Of selecting two CEOs and finding they both made more than $1 million?

a. Probability: 0.36 b. Probability: 0.57 c. Probability: 0.5714 d. Probability: 0.1190

Assume there are 12 homes in the Quail Creek area and 6 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 has a security system? c. What is the probability at least one of the selected homes has a security system? d. Are the events dependent or independent?

a. Probability: 0.9090 b. Probability: 0.9090 c. Probability: 0.9090 d. Dependent

Mookie Betts of the Boston Red Sox had the highest batting average for the 2018 Major League Baseball season. His average was 0.418. So, the likelihood of his getting a hit is 0.418 for each time he bats. Assume he has eight times at bat tonight in the Red Sox-Yankee game. a. This is an example of what type of probability? b. What is the probability of getting eight hits in tonight's game? c. Are you assuming his second at bat is independent or mutually exclusive of his first at bat? d. What is the probability of not getting any hits in the game? e. What is the probability of getting at least one hit?

a. Type of Probability: Empirical b. Probability: 0.001 c. Independent d. 0.13 e. 0.987

Refer to the following picture. a. What is the picture called? b. What rule of probability is illustrated? c. B represents the event of choosing a family that receives welfare payments. What does P(B) + P(∼B) equal?

a. Venn diagram b. Complement rule c. 1