In Class Exam 2 Review Math 141
1. Solve the linear programming problem. Find the maximum and minimum of
P=6x + 3y and the points where they are attained on the region bounded by
4x + 15y > 60, 2x + y > 12 and 4x + 5y < 40.
2. Does C = 5x + 8y have either a maximum or a minimum on the region bordered by y > 2, 6x + 7y > 74, 8x + 3y > 48 ? If not, why not and if so, find it.
3. True or False Use Venn diagrams to support your answer.
a) 
.
a) If 
, then 
.
4. The
universal set is the people in
T is all those in C.S who got a traffic ticket within a year.
A is all those in C.S. who had a traffic accident within a year.
S is all those in C.S. who have gone over the speed limit within a year.
Describe each set in words and shade it in a Venn diagram.
a) 
b) 
c) 
5. A company is studying the effectiveness of its advertising. 45 people who use the product were asked if they read the newspaper ad or watched the TV ad. Eight said they had done neither. A total of 20 people read the newspaper ad and a total of 32 people watched the TV ad. How many did both?
6. 70 children were asked if they own a cat, a dog or a guinea pig.
5 said they own none of these.
30 own a cat.
9 own a cat and a dog, but do not own a guinea pig.
2 own all three.
6 own a cat and a guinea pig.
20 own only a dog.
25 own a cat or a guinea pig, but do not own a dog.
a) Fill in a Venn diagram with the number in each region (all 8 regions).
b) How many own at least one of the three?
d) How many own a guinea pig?
7. Six friends sign up for a course which has 10 sections.
a) How many ways can they be assigned to sections?
b) How many ways can they all get different sections?
c) How many ways can at least two get the same section?
8. How many 5-long codes can be made from the first 12 letters of the English alphabet if letters which are next to each other cannot be the same?
9. Four
companies each send representatives to a convention. There are 4 from Honda, 3
from
a) How many ways can they line up for a photo?
b) How many ways can they line up for a photo if representatives of the same company must be kept together?
10. How many distinguishable arrangements are there of 18 new cars consisting of 4 silver Honda civics, 3 black Toyota corollas, 5 red Ford escorts, and 6 white Chrysler minivans?
11. Give a sample space for each experiment which is suitable for a uniform probability space.
a) Toss a fair coin 3 times and observe the number of heads.
b) Select 3 distinct letters from a set of 5 distinct letters.
12. a) Determine whether or not the table defines a probability distribution on S. S={a, b, c, d}.
Element of S a b c d
Probability 0 .12 0 .4 0 .2 0 .25
b) Fill in the missing probability so the table defines a probability distribution on
S= {a, b, c, d}
Element of S a b c d
Probability 0 .1 0 .2 0 .3
c) True or False
If 
then P(A)< P(B).
d) If A and B are any two
subsets of S with P(A)=0.5 and P(B)=0.8, can P(
13. a) What does mutually exclusive mean?
b) Is P
and when are they equal?
14. A fair coin and a 6-sided die are tossed. What is the probability the coin lands heads or the die lands with 2 on top?
15. A six sided die is tossed 9 times. What is the probability of getting exactly two “4”s?
16. A crate contains 15 oranges, 20 grapples and 10 pears. Seven are randomly chosen without replacement. How many outcomes correspond to the even that:
a) At least one orange is chosen?
b) 3 grapples and 4 pears are chosen?
c) Exactly 3 grapples or exactly 4 pears?