Advanced Quantitative Methods Winter 2009
Final Exam
Marks 1. You are dealt 4 cards from a standard deck of 52 cards.
(3) (a) How many ways can the first card drawn be a king and the remaining cards
are not kings.
(3) (b) How many ways can the first card drawn be a king and the remaining
cards are not aces.
(3) (c) How many ways can the first card drawn be a king and the remaining
cards are not hearts.
2. How many ways can a class of 25 students
(3) (a) Elect a president, vice president and treasurer?
(3) (b) Elect a committee of three to represent them?
(3) (c) Elect a president and two others?
3. A student council is made up of four women and six men. One of the women
is president of the council. A member of the council is selected at random to report
to the dean of student life.
(3) (a) What is the probability that a woman is selected?
(3) (b) What is the probability that a man is selected?
4. The Committee on Student Life did a survey of 417 students regarding satisfaction
with student government and class standing. The results follow:
Freshman Sophomore Junior Senior Total
Not Satisfied 17 19 23 12 71
Neutral 61 35 32 38 166
Satisfied 23 49 43 65 180
Total 101 103 98 115 417
Assume that the sample represents the entire population of students.
Find the probability that a student selected at random is
(3) (a) Neutral and freshman
(3) (b) Satisfied, given that the student is a senior
(3) (c) Senior, given satisfied
5. The following data are based on a survey taken by a consumer research firm.
In the table, x= number of televisions in household in household and
% = percentages of U. S. households
x 0 1 2 3 4 5 or more
% 3% 11% 28% 39% 12% 7%
(3) (a) What is the probability that a household selected at random has less than
three televisions?
(3) (b) What is the probability that a household selected at random has more than
four televisions?
