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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
Week in Review, Review for Exam 2
1. An experiment consists of observing the outcomes when you toss a coin and then randomly
select a marble from a jar filled with 3 identical red, 2 identical blue, and 5 identical green
marbles.
(a) What is the sample space for this experiment?
(b) Describe the event E that a red marble is drawn.
(c) Describe the event F that a tail is tossed or a green marble is drawn.
(d) Are E and F mutually exclusive events?
(e) How many events are there total?
2. A chef has 20 different recipes that she wants to arrange in her recipe book. She has 9 dessert
recipes, 6 entree recipes, and 5 appetizer recipes.
(a) How many ways are there to arrange all 20 recipes in the book?
(b) How many ways are there to arrange the recipes if she wants all the dessert recipes
together, all the entree recipes together, and all the appetizer recipes together?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
3. In a graduating class of 200 students, there will be one valedictorian, one salutatorian, and a
group of 18 others will be in the top ten percent of the class. In how many different ways could
the school have a valedictorian, salutatorian, and the rest of the top ten percent (assuming we
know nothing about grades.)
4. A bag of marbles consists of 7 red, 9 green, and 10 yellow. Suppose a sample of 6 marbles is
selected.
(a) How many samples would contain exactly 4 reds?
(b) How many samples would contain at least 3 green?
(c) How many samples would contain no green marbles?
(d) How many samples would contain exactly 3 yellow or exactly 2 red?
5. A grocery store stocker needs to stock a shelf with 7 identical cans of soup, 6 identical boxes
of cereal, and 5 identical bottles of ketchup. He is in Math 141, so he starts rearranging all the
items in a row in different ways. How many DIFFERENT arrangements are possible?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
6. Let U = {a, b, c, d, e, f, g, h, i, j}, A = {a, d, h, j}, B = {b, e, f, i}, C = {e, h}, and D = {a, j}.
Determine whether the following statements are True or False.
(a) TRUE
(b) TRUE
(c) TRUE
FALSE
FALSE
FALSE
D⊆A
C⊂B
g ∈A∪B
(d) TRUE
FALSE
(A ∩ B)c = U
(e) TRUE
FALSE
(B ∩ C) ∪ D = (f) TRUE
FALSE
n((A ∪ B)c ) = 2
(g) TRUE
FALSE
n((D ∪ C) ∩ A) = 4
(h) TRUE
FALSE
C and D are disjoint sets.
7. Find the number of different arrangements of each of the following words.
(a) teamworks
(b) tralaalaa
(c) lalaalaaa
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
8. How many 5-digit numbers are possible if the 1st, 3rd, and 5th digits must be odd, the 2nd
and 4th digits must be even, and there can be no repetitions.
9. A certain high school offers 3 AP exams: Calculus, U.S. History, and English. There are 185
students in the senior class. Data is given below of how many seniors took these AP exams.
17 seniors took English and History, but not Calculus.
30 seniors took only Calculus.
41 seniors took Calculus and History.
43 seniors took exactly 2 AP exams.
127 seniors took Calculus or English.
84 seniors took History.
25 seniors took all three AP exams.
(a) How many seniors did not take any of these AP exams?
(b) How many seniors took exactly 1 AP exam?
(c) How many seniors took Calculus or English, but not History?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
10. In how many different ways can 12 teachers and 2 substitute teachers be chosen from a pool of
23 candidates?
11. Let A and B be sets in the universal set U . If n(A) = 24, n(B) = 12 , and n(A ∪ B) = 32, find
(a) n(A ∩ B)
(b) n(U ) if n(Ac ∩ B c ) = 6
(c) n(Ac )
12. A student has to take one course in physics, three in literature and two in mathematics, or two
courses in physics, two in literature and one in mathematics. He may choose among 5 physics
courses, 9 literature courses and 8 mathematics courses. In how many ways can this student
select the courses he has to take?
13. Five cards are dealt from a standard 52 deck. In how many ways can two of the cards be
diamonds or three be hearts?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
14. Minimize C = 2x + 4y subject to:
x + y ≤ 10
x + 2y ≥ 14
x≥2
y≥0
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
15. The Corner Coffee Shop is selling two blends of beans: House Blend and Anniversary Blend.
House Blend is one-half Mexican beans and one-half Colombian beans. Anniversary Blend is
one-quarter Mexican beans and three-quarters Colombian beans. Profit on the House Blend
is $3.50 per pound, while profit on the Anniversary Blend is $4.00 per pound. Each day the
Corner Coffee Shop receives a shipment of 200 pounds of Mexican beans and 330 pounds of
Colombian beans to use for the two blends. How many pounds of each blend should be prepared
each day to maximize profit? What is the maximum profit?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
16. A glass dinnerware factory produces glasses and bowls, at its two plants, Plant A and Plant
B. Plant A produces 300 glasses and 200 bowls each day at a cost of $1000, while Plant B
produces 100 glasses and 600 bowls each day at a cost of $1500. Shannon has an order from a
local Supermarket for at least 30,000 glasses and 60,000 bowls. How should Shannon schedule
the production so that it can fill the order at minimum cost? What is the minimum cost?
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