Possible Outcomes of an Experiment
Do all the following problems.
I. Choose the best answer for each multiple choice. Please use CAPITAL letters to indicate your answer and write neatly. (20 points)
1. ____ 3.____ 5. ____ 7.____ 9. ____
2. ____ 4.____ 6. ____ 8.____ 10. ____
1. The volume that results in total revenue being equal to total cost is the
A. break-even point.
B. marginal volume.
C. marginal cost.
D. profit mix.
2. A list of all possible outcomes of an experiment is called
A. the sample space.
B. the sample point.
C. the experimental outcome.
D. the likelihood set.
3. Which of the following is not a valid representation of a probability?
A. 45%
B. 1.07
C. 0
D. 1/8
4. Which of the following is not a proper sample space when all undergraduates at a university are considered?
A. S = {in-state, out-of-state}
B. S = {freshmen, sophomores}
C. S = {age under 21, age 21 or over}
D. S = {a major within business, no business major}
5. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The complement of A is
A. all new customers.
B. all accounts fewer than 31 or more than 60 days past due.
C. all accounts from new customers and all accounts that are from 31 to 60 days past due.
D. all new customers whose accounts are between 31 and 60 days past due.
6. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The union of A and B is
A. all new customers.
B. all accounts fewer than 31 or more than 60 days past due.
C. all accounts from new customers and all accounts that are from 31 to 60 days past due.
D. all new customers whose accounts are between 31 and 60 days past due.
7. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The intersection of A and B is
A. all new customers.
B. all accounts fewer than 31 or more than 60 days past due.
C. all accounts from new customers and all accounts that are from 31 to 60 days past due.
D. all new customers whose accounts are between 31 and 60 days past due.
8. If P(AB) = 0
A. A and B are independent events.
B. P(A) + P(B) = 1
C. A and B are mutually exclusive events.
D. either P(A) = 0 or P(B) = 0.
9. The union of events A and B is the event containing
A. all the sample points common to both A and B
B. all the sample points belonging to A or B
C. all the sample points belonging to A or B or both
D. all the sample points belonging to A or B, but not both
10. If P(A) = 0.35, P(B) = 0.74, and P(A B) = 0.37; then P(A B) =
A. 1.21
B. 0.94
C. 0.72
D. 1.48
II. Problem Solving
1. A national survey indicated that 25% of adults conduct their banking online. It also found that 35% are under the age of 50, and that 22% are under the age of 50 and conduct their banking online.
a. What percentage of adults do not conduct their banking online? (6 points)
b. What type of probability is the 22% mentioned above? Just write down the name of the probability. (6 points)
c. Construct a joint probability table showing all joint and marginal probabilities. (10 points)
d. What is the probability that an individual conducts banking online given that the individual is under the age of 50? (8 points)
e. Are Banking Online and Age independent? Explain. (10 points)
2. A local university has a student population that is 55% male. 60% of students are undergraduates. 38% are both male and undergraduates.
a. What is the probability that a randomly selected student is both female and an undergraduate? (10 points)
b. What is the probability that a randomly selected student is either female or an undergraduate? (10 points)
3. As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000
Variable cost per occupied room per night $ 20
Revenue per occupied room per night $ 75
a. Write the expression for total cost per month. Assume 30 days per month. (4 points)
b. Write the expression for total revenue per month. (4 points)
c. How many rooms they need to sell per night in order to break even? (6 points)
d. Suppose 5 rooms can be sold per night, how much they should charge per night in order to breakeven? (6 points)