Download Name Math 1312 - Angelo State University

Name _____________________________ Math 1312.510 Short Quiz #1, July 8, 2002
1. Fill in the blanks.
a) A ________________ is a collection of objects having a well-defined property in common.
b) The objects (members) of a set are called ___________ of the set.
c) The set that contains all objects under consideration for each particular experiment is called the
__________________ set.
d) A set B is called a ______________ of a second set C provided every element in B is also in C.
e) Sets A and B are said to be equal provided _____________ and _____________.
f) A set is called the _____________ set or the _________ set if it does not contain any elements.
2. Which of these sets are well-defined.
a) Set of all students that have taken math 1311.  ___________
b) Set of all students that drove to school today  __________
c) set of all good-looking students in class  ____________
d) set of all smart students in class  _______________
3. Identify each of the following sets.
{ 1, 2, 3, .. } set of ____________________
{ 0, 1, 2, 3, … } set of _________________________
{ 2, 3, 5, 7, 11, … } set of ______________________________
{ … -3, - 2, - 1, 0, 1, 2, 3, … } set of __________________
Answers to qz #1.
1. a) set
d) subset
2. a) set
b) elements
e) A  B and B  A
b) set
c) universal set
f) empty set or the null set
c) not well-defined
d) not well – defined
3. a) set of natural numbers, set of counting numbers, or set of positive integers
b) set of whole numbers or set of nonnegative integers
c) set of prime numbers
d) set of integers
e) A  B and B  A
f) empty set or the null set
Additional questions –
1. Is 2  { 1, 2, 3 } ? ____________
Is { 2 }  { 1, 2, 3 } ? ___________
Is 2  { 1, 2, 3 } ? ___________
Is { 2 }  { 1, 2, 3 } ? ___________
2. True or False.
________________ a ) { 1, 2, 1 } = { 1, 2 }
________ b) { 1, 2 } = { 2, 1 }
3. Which name fits the following set { 0, 1, 2, 3, … }
set of positive integers,
set of natural numbers,
set of nonnegative integers
4. Which name fits the following set { 1, 2, 3, … }
set of positive integers
set of whole numbers
set of real numbers
5. { -2, - 1 } can be called the set of negative integers  ___________
6. What set could be used to describe the following situation
set of : whole numbers, natural numbers, rational numbers, irrational numbers, real
( select the smallest possible set )
a) the number of working pens in your pocket 
b) the value of the money in your pocket 
c) the exact amount of gas in a person’s car 
d) the number of red lights you have run this week 
Name _______________________ Math 1312 – Short Qz # 2, July 10, 2002
1. Two sets are said to be ________________ if they have no element in common.
The ____________ of sets A and B is the set that contain every element that is in either A or in B or
in both A and B.
The _________________ of A and B is the set that contains only the elements that are found in both
A and B at the same time ( the element must be in A and also in B )
The _________________ of a set A is the set that contains all of the elements in U ( the universal
set ) that are not in A ( outside of A )
2. Draw a Venn Diagram to represent
a) A  B
b) A  B
3. Shade the set that corresponds to A /  B
4. A set of real numbers is made entirely of numbers that are either _______________ or
_____________ numbers
5. Let A = { x : x is a whole number with x2 < 4 } and B = { x | x is an even prime number }
Find
a) A  B = {
}
6. True or False.
_______
a)
A  B = B  A for any sets A and B
________ b) A  ( B  C ) = ( A  B )  C
b) B  A = __________________
Answers to additional questions qz #1
b) no,  can only be use to compare sets to sets
1) yes
c) yes
2.
d) no,  can only be used to compare an element to a set
a) True: repetitions do not change a set
b) true: order does not matter
3. set of nonnegative integers: 0 is not positive
4. set of positive integers = set of natural numbers
5. false: { - 2, - 1 } represents only two numbers and yes they are both negative integers
6. a) { 0, 1, 2, 3, … }  set of whole numbers
b) { 3.25, 1.13, … }  set of rational numbers
c) real numbers
d) whole numbers
Answers to short qz #2
1. disjoint
b) intersection
c) complement of A
2. A  B : consists of all of A and all of B
b) A  B : intersection of A and B
3. A /  B : outside of A and at the same time inside of B ( only the portion of B that is outside of A)
4. rational or irrational
5. A = { 0, 1 }
B={ 2}
A  B = { 0, 1, 2 },
6. a) A  B = B  A,
b) no,
B A={ }
yes: union is commutative
Name ___________________________ Math 1312.510 , Short Quiz #3, July 10
1.
Let A = { a, b, c } and B = { 1, 2 }
since A x B = { (a,1), (a,2), (b,1), (b,2), (c,1), (c,2) },
a) then B x A = _________________________
b) What would A x A look like ? A x A = ___________________________________________
c) Find n( B x A ) = _____________
d) n( A x A x A ) = ___________________
2. A boy has three tasks to perform:
he will watch tv for ½ hour: he has four choices of TV programs
he has to eat breakfast: three choices of cereal
he can call a friend to come over: he has five different choices
How many different ways can he accomplish all three tasks together ? _________________
3. Shade the following sets
a)
A/
b) A/  B/
4. A twelve-sided die is tossed with each side labeled as 1 – 12. What is the likely hood in terms of a
fraction that a seven will be rolled ?
5. Find the value of the number x if
x + ½ + 1/3 = 1  x = ________
6. A sample of 100 drivers at an intersection showed that 40 turn left and 50 go straight. How many
actually turn ?
7. A class grade is determined by using four exams which are weighed equally and a final which counts
twice as much as one of the other exams. What fractional part of grade does the final count ?
Answers to qz #3
1. a) B x A : same as A x B except interchange the order--- B x A = { ( 1, a ), (2, a) ,…, ( 2, c ) }
b) A x A = { ( a, a ) , ( a, b ) , ( a, c ), ( b, a ) ,… , ( c, c ) }
c) n ( B x A ) = n(B )  n ( A ) = 2  3 = 6
d) n ( A x A x A ) = 3  3  3 = 27
2. ( 4 ) ( 3 ) ( 5 ) = 60
3.
a) A / : shade everything outside of A but still inside U.
b) A/  B / : Shade everything that is outside of A and at the same time it is also outside of B
4. 1 / 12
5. x = 1/ 6
6. 40 turn left, 50 go straight , which means 10 turn right  n( turn ) = n( turn right or left ) = 50
7. let x be the value of a regular exam: x + x + x + x + x + x = 1 ( the last two represent the final exam)
x = 1/6
Answers to Short Quiz #4 – July 11
0.1 uniform probability
1. a) S = { a, b, c, d, e, f }
c)
b) sample points  6 ( six possible outcomes )
26 = 64 gives all possible events including the empty set ( no letter is used )
answer = 64 – 1 = 63
2. Change the problem to read : six-sided die with faces --- 1, 1, 2, 2, 3, 3
a) S = { 1, 2, 3 }
b) 2 / 6 = 1/ 3
c) P( five ) = 0 , five is not possible – do not write 
answers to original question with possible faces: 1, 1, 2, 2, 2, 3
a) you can not find a sample space with uniform probability, the best you can do is S = { 1, 2, 3 }
b) P ( two ) = 3 / 6
3. certain event if prob = 1
4. 0  P( E )  1
c) P ( five ) = 0
impossible event if prob. = 0
The sum of the prob. of the sample points ( of the elementary events) = 1
5. have to add up to 1 – P(s1 ) = 0.1, P (s2) = 0.5  means P(s3 ) has to equal 0.4
Since E = {s2, s3 } , then P ( E ) = P ( s2 ) + P ( s3 ) = 0.4 + 0.5 = 0. 9
Name ___________________________ Math 1312 – Short Qz #5 – July 11, 2002
0.1 A sample space in which each outcome has the same probability is said to be equiprobable or it has
___________________ probability ( do not use the word equal )
1. A cube is rolled. The cube has the following letters on the sides (one per side)
-- a, b, c, d, e, and f
a) Write a sample space for this experiment  S = { _______________________ }
b) How many sample points does your sample space have ?  ___________
c) How many different events (words ) are possible using any number of letters ?
Keep in mind that in our case “word” means any group of letters – whether they make sense or not,
does not matter – but there has to be at least one letter in your word.
2. A six sided fair die is rolled. The faces are labeled – 1, 1, 2, 2, 2, 3, 4
a) Write a sample space that has uniform probability.  S = { ______________________ }
b) What is the probability that a two is rolled ? ______________
c) What is the probability that a five is rolled ? ______________
3. An event is said to be __________________ whenever its probability is equal to 1
An event is said to be ______________________ whenever its probability is equal to 0 .
4. Given any event E , _________  P ( E )  ________ .
The sum of the probabilities of the sample points (the elementary events ) must equal _______
5. Suppose we have the following sample space S = { s1, s2, s3 } with P(s1) = 0.1, P (s2) = 0.5
with E = { s2, s3 }. Find
a) P ( s3 ) = _______
P ( E ) = __________
Answers to this quiz are on the previous page
Name ____________________________ Math 1312.510 – Short Quiz # 6, July 17, 2002
1. Which of these sets best illustrates an example of two independent events.
2.
3. If A and B are mutually exclusive, find P(A | B ) = _____________
4. If A and B are independent, find P(A | B ) . __________________
Name ___________________________- Math 1312.510 – Short QZ #7 , July 18, 2002
Two events A and B are ___________________ if P(A  B ) = P(A ) P(B)
1.
If A  B = , we say A and B are disjoint or ___________________________
If P(A| B ) = P(A ) , we say that A and B are ______________
2. True or False.
a) If A and B are mutually exclusive, then A and B can not be independent  ___________
b) If A and B are independent, then A  B    ______________
c) If A and B are not independent, then they must be mutually exclusive  __________
3. Students have been known to make decisions independently from each other. A group of five students
is asked to volunteer to help with a project. Normally, the probability that a student will say yes is
0. 6
What is the probability that all of them say no ?  ________________
What is the probability that the fourth student will say no ?  ______________
What is the probability that the first two will say yes and the last three will say no ?  ___________
Answers:
1. a) independent
2. a) true
3. (0.4)5 = ____
b) mutually exclusive
b) true
c) independent
c) false
b) 0.4
c) (0.6)2 (0.4 )3 = ________
Name ______________________________ Math 1312 – Short Qz #8 – July 24, 2002
1. Complete the formulas
a) P(n,r) = ______________
b) C(n,r) = ______________
c) P( A | B ) = ________________
d) P( X = x ) if X is a binomial r.v.  ___________________ ( formula for a binomial experiment)
2.
A binomial experiment is given with n = 10, p = 0.2. Find the probability of having 3 successes.
3. Tires produced at a factory have a probability of 0.01 of being defective. A sample of five tires are
observed. What is the probability that
a) all are defective.
b) at least one is not defective.
c) exactly three are defective.
4. Four people are to be selected from a group of 6 men and 4 women. What is the probability that all
four are men ?
Name __________________________ Math – Short QZ – July 25, 2002
1. If A and B are independent events of some sample space S with P(A) = 0.4 and P(B) = 0.2, then
find
a) P(A | B ) = ____________
b) P(A  B ) = _______
2. Find the mode of the data: 2, 4, 2, 4, 3, 3, 2, 3, 2, 2, 5  _______
3. Find the median of : 2, 5, 3, 5, 4  _____________
4. Find the median of 4, 5, 7, 2  ____________
5. Find the arithmetic mean of the data: 2, 2, 4, 5, 5  ___________
6. Find the mode _________, the median ____________, and the arithmetic mean _________
of
4 occurs with frequency 15
7 occurs with frequency 20
10 occurs with frequency 25
Answer to short quiz # 8
1. a) P(n,r) = n! / ( n – r) !
b) C(n,r) = n !
c) P( A | B ) = P( A  B) / P(B)
/ (r!)(n-r)!
d) C(n,x)pxqn-x
2. C(10, 3)(0.2)3(0.8)7 = ___________
3. Binomial experiment, define s = event tire is defective , p = 0.01
b) 1 – P(all are defective ) = 1 – ans. from part a
a) C(5, 5)(0.01)5(0.99)0 = _________
c) C(5, 3)(0.01)3(0.99)2 = _________
4. C(6, 4) / C( 10, 4) , This is not a binomial experiment, can not use the binomial formula
ans. to short quiz #9
1. P( A | B ) = P(A ) = 0.4
b) P(A  B ) = P(A)P(B) = 0.08
2. mode: 2
3. median:4
4. median: ( 4 + 5) / 2 = 4. 5
5. mean: ( 2 + 2 + 4 + 5 + 5) / 5 = 18 / 5 = 3.6
6. a) mode : 10 since it has the largest frequency
b) median: 7 ( middle value)
c) a. mean:
[ 15(4) + 20(7) + 25( 10 ) ] / 60 = 450 / 60 = ________
Name __________________________ Math 1312 – Short QZ #10 – July 31, 2002
1. The total area under a normal curve = __________
2. The highest point of the normal curve is at its ___________________
3. If the mean of a normal curve is 40 and its variance is 25, then its standard deviation is ________
4. A normal curve with mean 40 and variance 16 has two inflection points; one at 44 and the other at ___
5. Find the inflection points of a normal curve with mean 40 and variance 9. ________ and ______
6. A standard normal curve has a mean of zero and a standard deviation of ________
7. The area to the right of 100 under a normal curve with mean 100 and variance 25 is __________
8. The area to the left of 105 under a normal curve with mean 100 and variance 25 is ___________
9. Find the following probabilities of a binomial r.v. with n = 100 and p = 0.1
a) The probability that X = 12  _____________________
** estimate the following by using a normal curve
b) The prob. that X > 12  _______________
c) The prob. that 10  X  12
Name _______________________ Math 1312.510 - Short Quiz #11, Aug. 2, 2002
1.
Identify as a slant line, a horizontal line, a vertical line, a parabola, an absolute value, or none of
these
a)
y – 4 = 0  ____________
b) y = x2 – 16  ________________
2. Sketch the graph of y = | x |
3. Let f(x ) = 2x – 3, find f( 2 ) = ___________,
4. Let f(x) = x / ( x + 2), find
find lim f(x) = ____________
x2
f( - 2) = _________ , find lim f(x) = ____________
x - 2
5. Let g(x) = 2/ ( x + 2 ), find lim f(x) = ____________
x2-
6. Find each of the following limits.
a) lim - 4 = __________
x ½
b) lim x = ____________
x3
c) lim x2 + 2
x 0 -
= ___________