Quiz: Chapter 15
Due: 19 September 2011
Name:
MA203J Contemporary Mathematics
Collaborators:
Instructions: Read every problem carefully.
• This quiz has two sides. Be sure to do them both!
• Write answers clearly in the space provided. Since this is a take-home quiz, you will be docked points
for messy or illegible answers. Hint: do your work on scratch paper first!
• You may use:
– your book, notes, claculator, and
– your classmates (in person or on the phone).
• You may not use:
– the internet (no Google or Wolfram Alpha; no email to anyone other than Kat),
– the Math Resource Center, or
– anyone other than your classmates or your instructor (Kat).
“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”
—S. Gudder
1. Seventeen students are running for three ASUN positions (president, vice president, and treasurer).
(a) (4 points) In how many ways can a president, vice president, and treasurer be elected? Use the
appropriate notation (n Cr or n Pr ) to do your calculations. Show all your work! (This means you
cannot use your fancy calculator to do all the work for you!)
(b) (4 points) After the election is over, in how many ways can a committee of four students be
selected from among the 14 losing students? Use the appropriate notation (n Cr or n Pr ) to do
your calculations. Show all your work! (Again, you may not use your fancy calculator to do all
the work for you!)
Quiz: Chapter 15
Due: 19 September 2011
MA203J Contemporary Mathematics
2. A 6-sided die is rolled 5 times in a row. The observation is how the die lands (1, 2, 3, 4, 5 or 6) on
each roll. For example, if you might observe 3, 4, 1, 1, 6.
(a) (1 point) Find a die and perform the experiment. (Hint: Most board games have dice.) Write
down your observation.
(b) (3 points) Use the multiplication rule to find the size of the sample space.1 Show your work!
3. (5 points) This question refers to the experiment in Problem 1. Write out the event described below.
E: “four or more of the rolls are a 3.”
4. (3 points) Find the probability of E from Problem 2. Show your work!
5. (3 points) Find the odds in favor of E. Show your work!
6. (2 points) Two points for turning in one food for thought.
7. (Bonus Point) An extra point if you turned in both!
1
If you are stumped, read Example 15.9 on page 560 and try drawing 5 boxes (Stage 1: first die roll; Stage 2: second die
roll; . . . Stage 5: fifth die roll) to help you figure out the answer.