Final Exam Advanced Quantitative Methods - 201-301-RE – December 2009 Page 1 of 3
Question 1 (6 marks)
You must calculate the number of ways in which ten persons can sit in a row.
a) Find the total number of possibilities.
b) What is the number of possibilities if two of the persons insist on sitting next to each other?
c) What is the number of possibilities if two of the persons do not get along and insist on sitting separately?
Question 2 (3 marks)
How many ways can you choose a project management team consisting of a project manager, a systems analyst and 3
programmers? There are 2 project managers, 4 systems analysts and 6 programmers to choose from.
Question 3 (10 marks)
We draw at random three marbles from a bag containing five red marbles, six blue marbles and two green marbles.
a) Find the probability of getting three red marbles.
b) Find the probability of getting two green marbles.
c) Find the probability of getting no blue marble.
d) Find the probability of getting one blue marble or one green marble.
e) Find the probability of getting one blue marble knowing that one green marble was drawn.
Question 4 (10 marks)
The following table shows how 558 people applying for a credit card were classified according to home ownership and
length of time in present job.
Less than 2 years 2 or more years Row total
Owner 73 194 267
Renter 210 81 291
Column total 283 275 558
Suppose that a person is chosen at random from the 558 applicants. We will use the following notation for events:
O: person owns home L: person has had present job less than 2 years
R: person rents home M: person has had present job 2 years or more
a) Compute P(O)
b) Compute P(O ∩M)
c) Compute P(O ∪M)
d) Compute P(R|L)
e) Are the events O and M independent? Explain.
f) Are the events O and M mutually exclusive?
Explain.
Question 5 (4 marks)
A class consists of 60% men and 40% women. Of the men, 25% are blond, while 45% of the women are blond. If a
student is chosen at random and is found to be blond, what is the probability that student is a man?
Question 6 (10 marks)
A franchise chain of small grocery stores has kept records of the number of bad checks passed in its stores. They used
the data to get a probability distribution for the number of bad checks passed in a store each week. In the table below X
denotes the number of bad checks and P(X) is the probability that X bad checks will be passed in a week.
X 0 1 2 3 4
P(X) 0.3 0.3 0.2 0.1 0.1
a) Calculate the expected number of bad checks the chain will get in one week.
b) Calculate the standard deviation for the number of bad checks.
c) What is the probability that two or more bad checks will be passed in a week?
d) What is the probability that no bad checks will be passed in a week?
e) How many bad checks should they expect to get in a given year?
Question 7 (11 marks)
The probability that a restaurant customer will request seating in the outdoor patio is 0.45. A random sample of 12
customers call to make reservations. Let X be a random variable denoting the number of customers that will ask to sit
in the outdoor patio.
a) Find the probability that five of them request outdoor seating.
b) Find the probability that fewer than three of them request outdoor seating.
