Question

1. 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 or both (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)?

2. Which NCAA college basketball conferences have the higher probability of having a team play in 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, these two conferences have both 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 a 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 one of these two conferences (to 2 decimals)?

Answer 1

1.) 0.54 ; 0.46

2.) 0.50 ; 0.40 ; 0.05 ; 0.85 ; 0.15

Explanation:

A = feel guilty about wasting food ; P(A) = 0.39

B = feel guilty leaving lights on ; P(B) = 0.27

Probability of feeling guilty for doing both = 0.12

P(AnB) = 0.12

1a.) 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 or both (to 2 decimals)?

P(AuB) = P(A) + P(B) - P(AnB)

= 0.39 + 0.27 - 0.12

= 0.54

1b.) What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

P(AuB)' = 1 - P(AuB)

P(AuB)' = 1 - 0.54

P(AuB)' = 0.46

2.)

n(ACC) = 10

n(SEC) = 8

n(total) = 20

n(ACC n SEC) = 1

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

n(ACC) / n(Total) = 10 /20 = 0.50

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

n(SEC) / n(Total) = 8/20 = 0.40

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

1 /20 = 0.05

d.)

P(AuB) = P(A) + P(B) - P(AnB)

= 0.50 + 0.40 - 0.05

= 0.85

e.)

P(AuB)' = 1 - P(AuB)

P(AuB)' = 1 - 0.85

= 0.15