Download Name Math 1312 - Angelo State University

Name __________________________________________ Math 1312.030
Short Quiz
Jan. 15, 2003
1. The set that contains all possible outcomes of a given experiment is called the ________________________ set of the
given experiment.
2. If A = { 1, 2, 3 } , we write __________ and say 2 is an object of A or
2 is an ___________________ of A
3. If A and B are any two given sets and every element of A is an element of B, we write ________________
and say A is a ________________ of B.
Two sets A and B are equal provided 1) __________________ and 2) ______________________
4. { 1, 2, 3, .... } is called the set of positive integers or the set of ___________________________________
5. The set { 0, 1, 2, 3, .... } is called the set of whole numbers or the set of ____________________ integers.
6.
Find the absolute value of
a)
| - 4 | = ______________
b) | 3 - 5 | = ________
7. Find all the elements of the given set.
a) A = { x | x is a whole number ≤ 4 } = ____________________________
b) B = { x | x is an integer and x 2 = 4 } = _________________________
c) C = { x | x + 4 = 2 and x is a natural number } = ___________________
8. True or False.
_____________ a)
_____________ b)
{3}
{ 1, 2, 3 }
{ 1, 2, 3 }
Name ___________________________________________ Math 1312 – Short Quiz #2, January 21, 2003
1. The set that contains all of the objects that are in A, in B, or in both A and B is called the _______________
of A and B and is written
_________
The set that contains all objects that can be classified as being in A and at the same time they are also in B is called
the ____________________ of A and B and is written ________________
The set that contains all objects in the universal set U that are outside of A, written A / , is called the _______________
of A
2.
How many subsets does the set A = { a, b, c, d } have ? ____________
3.
A group of 5 boys arrive at the local Jr. High.
How many different groups could be gathered by the Coke machine ?
___________________
4. Let A = { 1, 2, 3 }, B = { x | x > 2 } and U = { whole numbers less than 5 }
a) Find A U B = __________________________
b) A ∩ B = ________________
5. Shade the set that corresponds to
a) A U B
b) A/ ∩ B
Name ____________________________________________ Math 1312.050 – short quiz #3 – January 28, 2003
1. Event is to subset as __________________________ is to the universal set
2.
Mutually exclusive is the same as two sets being ____________________________
3. The elementary events of the sample space S = { s1, s2, s3 } are ________________________________
4. How many different events does the set S = { s1, s2, s3 } have ? ___________________
5.
If the elementary events of the sample space above are equally likely to occur , then we say that S has
___________________ probability.
6. Find x if
x + ½ + 1/3 = 1.
x = _________
7. A twelve sided die is rolled .
a) Write down a sample space.
S = { _________________________________ }
b) If your die has uniform probability, then find the probability of any of its elementary events. ____________
8.
A card is selected at random from a standard deck of 52 cards.
What is the probability that
a) the ace of hearts is drawn ? ___________
b) an ace is drawn ? _______________
c) an ace is not drawn ? ___________
Name ___________________________________________ Math 1312.030 -- Short Quiz #4 – Feb. 3, 2003
1. Another name for the set that is called a certain event is ___________________________________
2. True or False.
___________________ a. P(
) = 0
____________________ b. If E is any event of some sample space S, then the P(E) ≥ 0.
_____________________ c. If A and B are mutually exclusive, then n( A ∩ B ) =
______________________ d. If S = { s1, s2, s3 }, then P( {s1}) = 1/3
3. Let S = { s 1, s2, s3, s4 } with uniform probability then
a) P( S ) = __________
4.
b P ( s3 ) = _______________
If S = { s1, s2, s3 } with P ( s1 ) = 1/ 10, P ( s2 ) = 1 / 5 and E = { s2, s3 }.
a) Does S have uniform probability ? ___________________
b) What is P ( E ) = ? _________________
5. If E is an event of some sample space S with P(E ) = 3/7, then what does P( E / ) = ? _______________
6. A single card is drawn from a deck of 30 cards labeled 1-30. What is the probability that the card selected consists of at
least one even digit ? ex. 24, 23, 14,... Notice that 17 is not one of them.
_________________
7.
A group of 3 boys and 2 girls walk into the lobby. If they walked in one at a time in random order, then what is the
probability that a girl walked in first ?
______________
8. Consider all three child families with the children listed in order of birth.
a) Find a sample space.
b)
What is the probability that a family selected at random has two boys ?
_______________________________
_______________________
9. A class consists of 40 students; 23 male and rest female. 10 of the male students drive a car and 8 of the female students
also drive a car. A student is selected at random. What is the probability that the student drives a car ?
_________
If the student is known to drive a car, then what is the probability that the student is female ? ______
10. 30 students like the textbook, 20 like the notes, and 15 like both. How many like either one ( at least one ) ? _________
Name ________________________________ Math 1312.050 – Short Quiz # _________, February 11, 2003
1.
IF A and B are mutually exclusive events, then
a) P ( A ∩ B ) = __________
P( A | B ) = ____________
and the Venn Diagram looks like ?
2. If A and B are independent , then
a) P ( A | B ) = _____________
b) P ( A ∩ B ) = _______________
3. In general for any A and B,
a) P ( A | B ) = ___________
4.
b) P ( A ∩ B ) = ______________
A fair four-sided die (tetrahedral die) is rolled. The faces are labeled as 1, 2, 3, or 4.
Write a sample space of this experiment. S = { ___________________________ }
What is the probability that a three comes up ? ____________
5. Suppose that the die from above is rolled four times. You record the sequence of outcomes.
a) list one possible sequence _________________________
b) How many different sequences are possible ? _____________________
c) What is the probability that all four rolls come up “threes” ? ____________________
d) What is the probability that none of the rolls is a “three” ? _________________
e) What is the probability that at least one is a three ? ________________________
8. Use the tree diagram that follows to answer the following question.
P ( C ) = ____________
P ( D/ | A ) = __________
P ( D ) = _____________
Name _________________________________________ Math 1312 – short quiz # ____,
Feb. 18, 2003
1. Given the set { a, b, c, d } How many groups of three are possible ? ( order does not matter ) _______
Write them down : _______________________________________________________________________
2. From the same set above; how many permutations are possible using only three letters at a time ?
(order matters )
____________
3. Simplify. (without the use of a calculator )
a) 4 ! = ________
c) n ! / ( n +1 ) ! = ___________
4.
b) 0 ! = ______________
d)
350 ! / 349 ! = _____________
A committee is to be formed by selecting one member from each of the following three groups;
there are 40 staff members, 50 instructors, 20 administrators.
How many different committees are possible ? ________________
5.
Six blocks are labeled a, b, c, d, e, and f (one letter per block ). Four of the blocks are selected at random and
placed in a line ( left –to – right ) . How many different four-letter “words” are possible ?
______________
6. Three new executives will select an administrative assistant from a pool of 21. The selection is made in the order in
which they were hired. In how many different ways can the three positions be filled ?
___________________
7. A ______________________________ is a collection of n objects taken r at a time in which order matters and no
repetitions are not allowed.
8. A _____________________________ of a set of objects is a collection of n objects taken r at a time in which order
does not matter and repetitions are not allowed.
Math 1312 ---- Short Quiz # _________, Feb. 25, 2003 ------------------------- Name _______________________________
1. Find 0.6 + 0.7 + 0.4 = _________________ without a calculator.
2.
In our discussion of permutations and combinations: what is the main difference between them ?
3.
A = { a, b, c }
B = { b, c, d } ===>
Find A U B = ____________________
4.
If P ( A ) = 0.4
and P ( B ) = 0.3 , find P ( A U B ) = __________________ Why ?
5. If P ( A ) = 0.8 and P ( B ) = 0.5, find the smallest value that P ( A ∩ B ) = ? ____________________
6. In #5 above, what must P ( A ∩ B ) = ? if A and B are independent ? ____________________
Name ___________________________________________ Math 1312.030 – Short Quiz # ____, Feb. 27, 2003
1. Four boys and Four girls line up across each other.
Boy1 steps across and selects a dancing partner. Since these girls are sensitive and polite they will accept any of the four as
a dancing partner. Boy 2 goes next and so forth until all four boys have a dancing partner.
What is the probability that boy 1 is dancing with girl 1, boy 2 with girl 2, boy 3 with girl 3, and boy 4 with girl 4 ?
2. A young man is taking a five problem true-false quiz. He guesses at each question. What is the probability that he
a) gets all of the questions right ? _____________________
b) gets only one wrong (exactly one wrong) ? ______________
3. A young lady takes a five problem multiple choice quiz. Each problem has four choices. What is the probability that
she
a) gets all of them right ? ________________________
b) gets exactly one wrong ( exactly one wrong ) ? ________________
4.
A basket contains an apple, an orange, a carrot, a peach, a snicker bar, a heath bar, a almond bar, a coke, and a pack
of cigarettes. You are allowed to take four items (and you will ). Assume that fruit is good, the rest is bad.
What is the probability that
a) the four items you select will all be bad ? ____________________
b) three will be good and only one will be bad ? _______________________
5. Fifteen students are in class. Students walk out in random order. What is the probability that the students walked out in
some kind of alphabetical order ?
6. A single die is rolled four times. What is the probability that you have exactly one six ? __________________
None of the rolls are sixes ? ________________
7. Consider all five-card draws (poker hands ) with no replacement.
What is the probability that
a) you have exactly 2 aces and 3 face cards ? ________________________
a) you have exactly three aces ? __________________________
b) four diamonds and 1 is a club ? _______________________
b) You have at least one diamonds ? ______________________
8.
An office consists of 20 members 12 of which are male. Of the 12 male 8 happen to be nonsmokers while five of the
women can be classified as being nonsmokers. Four members are selected to represent the office all having the same
level of responsibility and
If the members are selected at random, What is the probability that
a)
all four are nonsmokers ? _____________________
b) exactly three are male members ? _____________________
c) If they are known not to be nonsmokers, all are male members ? ________________
9. Five blocks labeled: A, B, C, D, E
If a baby places three of them at random in a line from left to right, then what is the probability that the word
BED has been spelled ?
10. Consider all 5-card hands from a standard deck of 52 cards. What is the probability that all cards in your hand are
diamonds ?
11. A card is selected and the value is recorded. A second card is selected at random with the previous process repeated.
This continues until you have made five selections
What is the probability that you have selected five diamonds ?
Name ______________________________ Math 1312 – Short Quiz
1) List the three types of random variables that we are considering.
finite discrete, infinite discrete, and ______________________________
2) Classify each of the following in terms of the three types above.
a) Let the r.v. X represent the number of times that a person will say “well” during the a 1 minute interval.
What kind of r.v. is X ? ___________________________________
b) Let the r.v. Y represent the amount of time a person slept during the last 12 hours.
What kind of r.v. is X.
3.
Given 1, 5, 9 find
The arithmetic mean: _________________
4.
the average squared deviation ( variance ) _________________
Which of these would you expect to have the largest variance
4, 10, 16
or
80, 86, 92
or
same
or
not enough information
Name ___________________________________ Math 1312 – Short Quiz – April 1, 2003
1. A standard normal curve is normal curve with mean (µ ) = __________ and standard deviation (σ ) = ________
2. Find both inflection points of a normal curve with µ = 200 and σ2 = 25
______________
_______________
3. If a normal curve has µ = 100 and σ = 9, then
a) what is its variance ? _____________
b) what is the area to the left of 91 ? ____________
4. Find the area to the right of 2 under a standard normal curve. __________________________
z = 2.00
5. Use the formula
x -µ
z = --------------σ
to find the value z if x = 20 and µ = 25 with σ = 4
_________________
6. Find the area to the right of 20 under a normal curve with µ = 25 and variance = 16. __________________
Name ______________________________________ Math 1312 – Short Quiz – April 3, 2003
1.
True or False.
___________ a) the area underneath a normal curve can not exceed 1.
___________ b) a standard normal curve is a normal curve with µ = 1 and σ = 0
___________ c) The inflection points of a normal curve are always one standard deviation (σ ) away from the mean (µ )
2. If a normal curve has µ = 20 and it has standard deviation σ = 6. then find a positive value of x that is 4 standard
deviations away
3.
Which of the following represent Relations, Functions, Both, or Neither
a)
b)
c)
d)
4. What is the domain of
3a) _____________________________________
3d) _________________________________
5. What is the range of
3a) _____________________________________
3c) __________________________________