Name ______- Math 1312 – Long Quiz # 1, July 9, 2002
1. Complete each of the following blanks.
a) A ______of objects is a group of objects having a well-defined property in common
b) Two sets are said to be ______if they have no element in common.
c) The set that contains all elements under consideration the given experiment is called the
______
d) We say A and B are ______provided A Ì B and B Ì A.
e) The complement of A written A / represents the set that contains all element in the universal set U
that are
______
f) the ______is the set that contains no objects.
g) The ______of A and B is the set that contains all the objects that are found in A and
at the same time they are also found in B.
h) A set of real numbers is made up entirely of rational and ______numbers.
2. Shade the set that represents A Ç B using a Venn Diagram.
3. Let U = set of integers and
A = { x : x2 < 4 } B = { x : x is a negative integer }, C = { x : x is a natural number }
a) Find A = { ______},
b) Find B / = { ______}
c) Find B È C = { ______}
4. A game consists of selecting one of six playing pieces, one of four starting points, and a choice of
two types of directions. How many different ways could the first player begin this game ?
5. Let U = { 1, 2, 3, 4, 5 } with A = { x : x is even }, B = { x : x < 4 }, C = { x : x2 £ 4 }
a) Find A È B = ______b) Find A x B = ______
c) Find n ( A Ç C ) = ______d) Find n ( A x B ) = ______
6. Identify each of the following sets.
a) { 1, 2, 3, … } è ______
b) set of real numbers that only contain fractions and integers è ______
c) Describe the following set in words { - 2, -4, - 6, … }
è the set of ______
7. Which name best fits the set { 0, 1, 2, 3, .. }
the set of positive integers set of natural numbers set of nonnegative integers
8. True or False.
______a) 2 Î { 1, 2 } ______b) { 4 } Î { 1, 4 }
9. Is the set A = { x | x is a big number } a “ good” set ? Why or Why not ?
10. Use sets to describe the following shaded portion.
Name ______Math 1312.510 – Long Quiz #2, July 12, 2002
1. Let E be a given event of some sample space S. If S is known to have uniform probability, then we
define the probability of E by
P( E ) = ______
2. If S = { s1, s2, s3, … s10 } has uniform probability and E = { s2, s5, s7 }, then find P(E) = ______
3. In general for any event E of some sample space S, ______£ P(E) £ ______
4. A group consists of 20 students from which one representative is to be chosen. The group consists of
exactly 12 male students. What is the probability that the representative will be a female student if the
student is chosen at random ?
5. An ice cream vendor wants to know how many different two-scoop cones he is able to make based
on the fact that a customer has a choice of the
type of cone: plain, sugar-coated, cup, extra- large cone
ice-cream: strawberry, vanilla, chocolate, banana nut, mystery topping
How many different cones are possible ?
6. A universal set is to sets and counting as a ______is to probability
An ______is any subset of the set S of some experiment.
7. A single card is drawn from a standard deck of cards. What is the probability that the card is either a
diamond or a black card ?
8. Complete the following formulas.
a) n(A È B ) = n(A ) + ______- ______
b) P(A È B ) = ______
c) P ( A ) + P (A / ) = ______
d) n(A/ ) = n(S ) - ______
9. A room is filled with executives from 20 different companies 12 are male and 8 are female.
4 of the male members are known to have an advanced degree while only 3 of the female members
have an advanced degree. A person is chosen at random. What is the probability that the person
selected is
a) a woman è ______b) a woman with an advanced degree è ______
c) a man or a person with an advanced degree è ______
d) a man if the person is known to have an advanced degree è ______
10. A group of 20 students show up to class.
16 of the students are wide awake, 12 of the students are prepared for the exam, and 2 are neither
wide awake nor do they happen to be prepared.
A student is selected at random.
a) How many of the students are prepared and wide awake ? è ______
b) What is the probability that the student selected is wide awake but not prepared for the exam ?
è ______
11. A coin is tossed twice.
a) Write a sample space è S = ______
b) If the coin is fair , the what is the probability that both tosses are identical (same outcome ) ?
è______
12. In the preceding example. If the coin was loaded, say three out of 10 times it falls heads, then what
is the probability that in the next toss the outcome will be a tails ?
è ______
Answers to
Long QZ #1 summer II
1. a) set b) disjoint c) universal set d) equal
e) outside of A f) null set g) intersection h) irrational
2. shade the intersection of A and B
3. a ) A = { - 1, 0 , 1 } b) B / = { 0, 1, 2, 3, .. } c) { … - 3, -2, - 1, 1, 2, 3 … }
4. ( 6)(4)(2) ==> 48 : one of six, one of four, one of 2
5. a ) { 1, 2, 3, 4 } b) { ( 2, 1), ( 2, 2 ), ( 2, 3 ), (4, 1), ( 4, 2) , ( 4, 3) }
c) 1 d) 6
6. a) set of natural or counting numbers b) set of rational numbers
c) set of even negative integers
7. { 0, 1, 2, .. } -- set of nonnegative integers
8. a) true b) false, you can not compare set { } with the symbol Î
9. “ big “ is not well defined
10. – I can not remember the graph – but I think the answer was A È B
Long Quiz #2 - summer II
1. n(E ) / n( S ) 2. 3/10 3. between 0 and 1
4. 8/20 5. (4)(5)(5): cross product of A x B x B , you want n(A x B x B )
6. a) sample space b) event 7. 39 / 52
8. a) n(B) - n( A Ç B ) b) P(A ) + P(B) – P(A Ç B )
c) 1 d) n(A)
9. a) 8/20 b) 3/20 c) 15/20 d) 4/7
10. a) 10 b) 6/20
11 a) { hh, ht, th, tt } b) 1//2 12. 7/10
Name ______Math 1312.510 – Long Quiz #3, July 19, 2002
1. Find the formula:
a) P( A È B ) = ______
b) P( A | B ) = ______
2. If events A and B are mutually exclusive, then P ( B | A ) = ______
3. Which of these Venn Diagrams best illustrate independent events ?
4. If A and B were independent events with P(A ) = 0.4 and P( B ) = 0.2 , then find
a) P( A È B ) = ______b) P( A Ç B ) = ______
5. Company is trying to get approval of a certain drug. Approval must be given by three different
agencies; A, B, and C. They make their decisions independently from each other.
If the probability that the company gets approval from A is 0.4, from B is 0.2, and from C is 0.3,
then what is the probability of getting past all three agencies ?
6. A card is picked at random from a standard deck of cards (52). The card is then replaced and the deck
is reshuffled. A card is picked again. The pattern continues. What is the probability of drawing
a) four aces in four draws ? ______b) no aces in four draws ? ______
7. Find the value of 4! ______0 ! = ______200 ! / 199 ! = ______
8. A permutation of a set { a, b, c, d, e } is an arrangement of the objects of the set so that
1) the arrangement has no repetitions and 2) ______
9. A combination of the same set above is an arrangement of the objects of the set so that
1) the arrangement has no repetitions and 2) ______
10. A room is to be painted. The walls can be painted in any one of three colors, the ceiling in one of
two colors, and the trim can be one of five choices. How many different ways can the room be
done ?
11. Can the events A and B be independent if P( A ) = 0.8 and P(B ) = 0.5 ? Why or Why not ?
Math 1312 – Long Quiz #4 – Name ______, July 23, 2002
1. Complete each of the following formulas.
a) P(n, r) = ______b) C( n, r ) = ______
2. Find 200 ! / 201 ! in fraction form = ______0 ! = ______
3. 10 distinct flags are available to make a sign ( message) on a flagpole. Four flags are used to signal.
How many distinct messages are possible ? ( HINT: obviously if the red flag is on top, it will have a
different message than being on the bottom. )
______
4. A die is rolled four times and the sequence of outcomes is recorded. What is the probability that the
sequence consists of no sixes ?
______
5. A 4-problem matching quiz is given. There are four questions with 10 total possible matches.
Each answer can only be used once. How many different responses are possible for each 4-problem ?
______
6. A department consists of 20 women and 30 men. Each of the 50 can be classified in one-and only
one of each of the following; there are 3 accountants, 4 managers, 5 sales
people, and the rest are service workers. A committee of three is to be chosen. What is the
probability that
a) all are women ? ______b) None is a manager ? ______
c) exactly 2 are in sales ? ______
7. A Bernoulli experiment consists of two outcomes a ______and a ______
8. A die is rolled five times. What is the probability that your outcome consists of three – sixes ?
a) What is the Bernoulli Experiment ? ______
b) What is the success ? ______
c) What is the success probability ? ______
d) What is the probability that the outcome consists of three – sixes ?
Answers to long quiz # 3:
1. a) P( A È B ) = P(A ) + P(B) – P(A Ç B ) b)P(A | B ) = P( A Ç B ) / P( B )
2. P( B | A ) = 0 if A and B are mutually exclusive
3. Independent events: there is an intersection, but not every pair of sets that intersect represent
independent events
4. P( A Ç B ) = P( A ) P( B ), since they are independent è ( 0.4) ( 0.2 ) = 0.08
P( A È B ) = P ( A ) + P( B ) - P(A Ç B ) = 0. 4 + 0.2 - 0.08 = ______
5. independent events: P ( A Ç B Ç C ) = P(A ) P(B ) P© = (0.4)(0.2)(0.3 ) = 0.024
6. ( 4/52)4 b) ( 48/52)4
7. 4 ! = 24 b) 0 ! = 1 c) 200
8. permutation: order matters 9. combination: order does not matter
10. ( 3) (2)( 5) = 30 11) yes: if P(A Ç B ) = (0.8)(0.5) = 0.4
Answers to long Quiz # 4
1. see answers in short quiz #8 or #9
2. 1/ 201 b) 1
3. (10)(9)(8)(7) = ______or P(10,4) = _____
4. ( 5/6) 4 5. 10(9)(8)(7) = ______
6. C(20, 3) / C(50, 3) = ______b) C( 46, 3) / C( 50, 3)
c) C(5, 2) C(45, 1) / C(50, 3 )
7. a success and a failure
8. A die is rolled b) s = a six comes up c) p = 1/6 d) C(5, 3)(1/6)3(5/6)2
Name ______- Math 1312 – Long Quiz # 1, May 30, 2002
1. Complete each of the following blanks.
a) A ______of objects is a group of objects having a well-defined property in common
b) Two sets are said to be ______if they have no element in common.
c) The set that contains all elements under consideration the given experiment is called the
______
d) We say A and B are ______provided A Ì B and B Ì A.
e) The complement of A written A / represents the set that contains all element in the universal set U
that are
______
2. Let U = set of integers and
A = { x : x2 < 4 } B = { x : x is a negative integer }, C = { x : x is a natural number }
a) Find A = { ______},
b) Find B / = { ______}
c) Find B È C = { ______}
3. A hamburger is to be made consisting of meat and any of the following toppings
{ lettuce, cheese, tomatoes, pickles }. How many different hamburgers are possible if at least one
topping must be included ( meat plus something else ) ?
4. A game consists of selecting one of six playing pieces, one of four starting points, and a choice of
two types of directions. How many different ways could the first player begin this game ?
5. Let U = { 1, 2, 3, 4, 5 } with A = { x : x is even }, B = { x : x < 4 }, C = { x : x2 £ 4 }
a) Find A È B = ______b) Find A x B = ______
c) Find n ( A Ç C ) = ______d) Find n ( A x B ) = ______
Name ______Math 1312.010 – Long QZ – June 4, 2002
1. Complete the following blanks.
Another name for a subset of a sample space is an ______.
Two events are said to be mutually exclusive whenever the events are ______
An event A so that P(A ) = 0 is called what type of event ? an ______event.
2. Complete the following properties of the probability of a sample space S
with S = { s1, s2, s3 } and E = { s2, s3 }.
a) P ( s1 ) + P ( s2 ) + P ( s3 ) = ______
b) List any elementary event ( an event not a sample point ) of this given set S. ______
c) If F is any event of S, then _____ £ P ( F ) £ ______
3. Use the sample space S from # 2 above. If S has uniform probability, then what is P ( s2 ) ? _____
4. If S from #2 is not known to have uniform probability ( it may ), but P ( s1 ) = 0.2, then what is
P ( E ) = ______?
5. Let S = { s1, s2, s3 } with P ( s1 ) = 0.4, P ( s 2 ) = 0. 5, and P ( s3 ) = 0. 6 , with E = { s2, s3 }
What would you say about P ( E ) ? Why ?
6. A pair of dice is rolled . What are the odds in favor of getting a sum greater than 10 ? ______
7. A single card is drawn from a standard deck of cards. What is the probability that the card is
a) an ace ? ______b) a heart ? ______c ) an ace or a king ? ______
8. If the probability of passing this quiz is 0.9, then what is probability of not passing ? ______