BUSI Chapter 5 HW (Study Guide)

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed the following: Primary Color - # of opinions Red - 90 Orange - 84 Yellow - 48 Green - 89 Blue - 39 Indigo - 48 Violet - 2 What is the probability that a designer does not prefer blue?

0.9025

A board of directors consists of sixteen men and seven women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?

1/253, or 0.004

Solve the following: 22!/18!

175,560

Solve the following: 6C5

6

Solve the following: 8P5

6,720

A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is randomly chosen as the spokesperson?

Classical

You purchase a ticket for the Lotto Canada lottery. Over thirteen million tickets were sold. What is the likelihood you will win the $3 million jackpot?

Classical

A baseball player gets a hit in 38 out of 118 times at bat. The probability is 0.32 that he gets a hit in his next at bat.

Empirical

The probability of an earthquake in northern California in the next 12 years above 13.0 on the Richter Scale is 0.84.

Empirical

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.

Number of Possible Outcomes: 4

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. CEO>$1M CEO<$1M Total SMM 4 11 15 SLM 7 8 15 --------------------------------- Total 11 19 30 {*Key: SMM-shareholders made money SLM - shareholders lost money CEO>$1M - CEO made more than $1 million CEO<$1Mil - CEO made less than $1 million.} If a company is randomly selected from the list of 30 studied, what is the probability: a. The CEO made more than $1 million? (Round your answer to 2 decimal places.)

Probability 0.37

A student is taking two courses, history and math. The probability the student will pass the history course is 0.56, and the probability of passing the math course is 0.57. The probability of passing both is 0.41. What is the probability of passing at least one? (Round your answer to 2 decimal places.)

Probability is 0.72. Solution: 0.56 + 0.57- (0.41) = 0.72

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? (Round your answer to 2 decimal places.)

Probability is 0.81. Solution: P(A and B) =P(A)*P(B) P(A and B) = 0.90 *0.90 P(A and B) = 0.81

Assume there are 13 homes in the Quail Creek area and 6 of them have a security system. Three homes are selected at random: What is the probability none of the three selected homes has a security system. (Round your answer to 4 decimal places) Are the events dependent or independent?

Probability: 0.1223 Events are Dependent.

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. 2,024 b. Probability is 0.125 Solution for a: = 24C3 =24!/(24-3)!3! =2,024 for b: Combinations with the contaminated can =23C2 =23!/(23-2)!2! =253 Probability =253/2024 =0.125

Mookie Betts of the Boston Red Sox had the highest batting average for the 2018 Major League Baseball season. His average was 0.466. So, the likelihood of his getting a hit is 0.466 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. Are you assuming his second at bat is independent or mutually exclusive of his first at bat?

a. Empirical b. Independent

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: https://tinyurl.com/studysettiny 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? (Round your answer to 4 decimal places.) b. What is the probability of selecting a junior-college student? (Round your answer to 4 decimal places.) c. If the student selected is a four-year-college student, what is the probability that the student prefers ice skating? (Round your answer to 4 decimal places.) d. If the student selected prefers snowboarding, what is the probability that the student is in junior college? (Round your answer to 4 decimal places.) e. If a graduate student is selected, what is the probability that the student prefers skiing or ice skating? (Round your answer to 4 decimal places.)

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

A study of 228 advertising firms revealed their income after taxes: Income after Taxes | # of Firms Under $1 million | 112 $1 mil. to $20 mil. | 58 $20 mil. or more | 58 a. What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.) 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? (Round your answer to 2 decimal places.)

a. Probability - 0.49 b. Probability - 0.51

The events A and B are mutually exclusive. Suppose P(A)= 0.44 and P(B)= 0.43. a. What is the probability of either A or B occurring? (Round your answer to 2 decimal places.) b. What is the probability that neither A or B will happen? (Round your answer to 2 decimal places.)

a. Probability of either A or B is 0.87. b. Probability of neither A or B is 0.13. Solution: For a: P(A or B) = P(A)+P(B) = 0.44 +0.43 = [ 0.87 ] For b: P(neither A nor B) = 1- P(A or B) = 1 - 0.87 = [ 0.13 ]

A sample of 53 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. 38 of the 53 executives responded "yes". Based on these sample responses, what is the probability that an oil industry executive will respond "yes"? (Round your answer to 2 decimal places.) d. What concept of probability does this illustrate? e. Are each of the possible outcomes equally likely and mutually exclusive?

a. The survey of [ 53 ] people about environmental issues b. -33 people respond "Yes." - 39 people respond "Yes." - 28 people respond "No." -The questionnaire fails to reach one executive. c. Probability is 0.72 d. Empirical e. The outcomes are equally likely and are also mutually exclusive.

Refer to the following picture. (B) ~B *Key: (B) -circle with "B" inside 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. P(B) + P(~B) = 1