Chapter 4 Exercise Solutions

Chapter 4 Exercise Solutions 

Question 1

In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico (National Hurricane Center website, August 21, 2012).

a.  What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico (to 2 decimals)?

b.  Two days later, the National Hurricane Center projected the path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico. Hurricanes that reach the Gulf of Mexico have a .08 probability of having passed over Cuba. Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed over Cuba.

How did passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico? Use the above probabilities to answer this question.

P(C|H)	(to 2 decimals)
P(C|T)	(to 2 decimals)
P(H|C)	(to 4 decimals)

c.  What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba?

Select Increased to Dropped from Item 5   (to 2 decimals) to  (to 4 decimals).

Question 2

A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E₁) = .10, P(E₂) = .15, P(E₃) = .40, and P(E₄) = .20.

Are these probability assignments valid?
Select Yes, they are greater than or equal to 0 Yes, they are greater than or equal to 0 and sum to 1 Yes, they are greater than or equal to 0, but do not sum to 1 No, they are greater than or equal to 0 No, they are greater than or equal to 0, but do not sum to 1 None of the above  

Question 3 

Suppose an experiment has five equally likely outcomes: "E₁, E₂, E₃, E₄, E₅". Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied.


What is the probability of each experimental outcome (1 decimal)?


What method did you use to assign probabilities to the experimental outcomes?
Select Classical method Relative frequency method Subjective method Item 2

question 4

Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this question (CBS News website, December, 2014). Consider the responses by age groups shown below. Age Response 18–29 30+ Yes 134 293 No 131 432 Unsure     2     8 a.  What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? b.  What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? c.  For a randomly selected respondent, what is the probability that a respondent answers yes (to 3 decimals)? d.  Based on the survey results, does there appear to be a difference between ages 18-29 and 30+ regarding concern over global warming? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Yes, there is difference between ages 18-29 and 30+ regarding the concern over global warming becuase the probabilities of part a) and part b) are different.

Question 5

How many permutations of three items can be selected from a group of six?

Question 6

An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?

Question 7

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 80% of the successful bids and 44% of the unsuccessful bids the agency requested additional information.

a.    What is the prior probability of the bid being successful (that is, prior to the request for additional information)?
 

b.    What is the conditional probability of a request for additional information given that the bid will ultimately be successful?
 

c.     Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).

Question 8

The Eco Pulse survey from the marketing communications firm Shelton Group asked individuals to indicate things they do that make them feel guilty (Los Angeles Times, August 15, 2012). Based on the survey results, there is a .39 probability that a randomly selected person will feel guilty about wasting food and a .27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room. Moreover, there is a .12 probability that a randomly selected person will feel guilty for both of these reasons.

a.  What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room (to 2 decimals)?

b.  What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

question 9

Which NCAA college basketball conference has the higher probability of having a team play in a college basketball's national championship game? Over the last 20 years, the Atlantic Coast Conference (ACC) ranks first by having a team in the championship game 10 times. The Southeastern Conference (SEC) ranks second by having a team in the championship game 8 times. However, both conferences have had teams in the championship game only one time, when Arkansas (SEC) beat Duke (ACC) 76–70 in 1994 (NCAA website, April 2009). Use these data to estimate the following probabilities.

a.  What is the probability the ACC will have a team in the championship game (to 2 decimals)?

b.  What is the probability the SEC will have team in the championship game (to 2 decimals)?

c.  What is the probability the ACC and SEC will both have teams in the championship game (to 2 decimals)?

d.  What is the probability at least one team from these two conferences will be in the championship game? That is, what is the probability a team from the ACC or SEC will play in the championship game (to 2 decimals)?

e.  What is the probability that the championship game will not have a team from either of these two conferences (to 2 decimals)?

question 10

A company that manufactures toothpaste is studying five different package designs. a.    Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs (to 2 decimals)?   b.    In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Number of Design Times Preferred 1 5 2 15 3 30 4 40 5 10 d.    Do the data confirm the belief that one design is just as likely to be selected as another? Select Yes, the data confirm this belief No, the data do not confirm this belief Item 2   e.    Based on the actual experiment, what probability would you assign to each package design (to 2 decimals)? Design Probability 1 2 3 4 5 f.       g.    Which package design has the highest probability of selection by a customer? Select Design 1 Design 2 Design 3 Design 4 Design 5 None, they all have the same probability Item 8