Lenarz
Math 102
Extra Credit Problems
Due: December 11, 2012
Name:
Directions: You may earn up to 5 points of extra credit in each section towards the corresponding exam - for example, the problems from chapter 2 can earn you up to 5 points
of extra credit toward your Exam 1 score. Your exam scores may NOT exceed 50 points
(100%). You MUST use good notation and show appropriate work. It is possible to earn
partial credit.
Chapter 2 - Set Theory - points toward Exam 1
1. Represent each set by shading a Venn diagram.
(a) (1 point) A ∪ (B − C)
(b) (1 point) (A ∩ B) − C
2. Use the following information to answer the given questions:
n(A ∩ C) = 11,
n(B ∪ C) = 34,
n(A ∩ B ∩ C) = 5,
n(A ∩ B) = 10,
n(B ∩ C) = 8,
n(A ∪ B ∪ C) = 54,
n(C − A) = 10,
n(C 0 ) = 64
(a) (1 point) How many elements are in A − C?
(b) (1 point) How many elements are in B 0 ?
3. (1 point) A survey was taken of drivers regarding the factors that they considered important in buying a new car.
• 84 said cost.
• 15 said cost, but not gas mileage.
• 72 said safety.
• 48 said cost, gas mileage, and safety.
• 56 said cost and safety.
• 25 said gas mileage, but not safety.
• 20 said gas mileage, but not cost.
How many people said gas mileage in the survey?
Chapter 3 - Logic - points toward Exam 2
4. Determine if the following pairs of statements are logically equivalent.
(a) (1 point) ∼ (p ∨ ∼ q); ∼ p ∧ q
(b) (1 point) (∼ p ∨ ∼ q) ∧ (∼ p ∨ q); ∼ p ∧ q
5. If p is true, q is false, and r is true, then what is the truth value of each of the following:
(a) (1 point) (p ∨ ∼ q) → ∼ q
(b) (1 point) (∼ p ∧ q) → ∼ r
Math 102
Due: December 11, 2012
Page 2
6. (1 point) Use an Euler diagram to determine if the syllogism is valid or invalid:
Some poets are sensitive.
No sensitive people are selfish.
Brittany is a poet.
Therefore, Brittany is not selfish.
Chapters 13 & 14 - Counting & Probability - points toward Exam 3
7. A bin contains a total of 20 batteries, of which 6 are defective. If you select 2 at random,
without replacement, determine the probability that
(a) (1 point) none of the batteries selected are good.
(b) (1 point) at least one of the batteries selected is good.
8. (1 point) Five green apples and seven red apples are in a bucket. Five apples are selected
at random, without replacement. Determine the probability that two green apples and
three red apples are selected.
9. (1 point) The probability that a person is accepted for admission to a specific university
is 0.3. Determine the probability that exactly three of the next five people who apply
to the university get accepted.
10. (1 point) To play the game 4-spot Keno at a casino, a player pays $1 to play and must
select four numbers between 1 and 80. The order in which the numbers are selected is
not important. After the player has made his or her selection, the casino holds a drawing
and twenty of the eighty numbers between 1 and 80 are declared “winning numbers.”
The $1 bet is not returned to the player. The amount of money the player wins is given
by the following
Outcome
0 or 1 winning number
2 winning numbers
3 winning numbers
4 winning numbers
What is the expected value of a $1 bet?
Payoff
$0
$1
$4
$112