M118 Chapter 3
Goals
We have already learned the definition of probability and some
of its properties, such as that the sum of the probabilities of
all outcomes is 1, and that the probabilities of an event and
its complement add to 1. We also learned to u
1
Week 14
Chapter 8. Markov Chains
8.1. States, transitions, transition diagrams and transition matrices
Recall:
An experiment is an activity that results in a well defined outcome.
The sample space is the set of possible outcomes.
A stochastic process
1
Week 14
Chapter 8. Markov Chains
8.1. States, transitions, transition diagrams and transition matrices
Recall:
An experiment is an activity that results in a well defined outcome.
The sample space is the set of possible outcomes.
A stochastic process
Exam 3-Answer key
Identify your version using the answer choice (A) in Problem 1.
Version
Version
Version
Version
1:
2:
3:
4:
(A)
(A)
(A)
(A)
440
The system has no solution
x = 2, y = 3, z = 1
$50
Version1 Version2 Version 3 Version 4
1C
1E
1E
1B
2A
2A
2C
MIDTERM-Answer key
Version 1: Problem 1. A)
1
2
Version 2: Problem 1. A)
1
15
Version 3: Problem 1. A) 13
Version 4: Problem 1. A) 16
Version1
1E
2A
3A
4D
5C
6D
7E
8C
9C
10D
11A
12B
13C
14E
15B
16D
17A
18D
19B
20B
21B
22B
23E
24B
25A
Version2
1A
2B
3D
4E
Exam 1-Answer key
Version
Version
Version
Version
1:
2:
3:
4:
Version1
1B
2A
3E
4A
5A
6B
7B
8D
9E
10E
11D
12C
13A
14D
15A
16D
17D
18B
19D
20C
Problem
Problem
Problem
Problem
1
1
1
1
Version2
1A
2A
3E
4C
5E
6C
7C
8E
9A
10D
11A
12E
13A
14A
15D
16E
17A
18C
1
1
Exam 3 - Review
Chapter 5: Systems of linear equations
lines, slope, intercepts(to find the x-intercept, set y = 0 and solve
x, to find the y-intercept, set x = 0 and solve y) point-slope form
(y y1 = m(x x1 ), slope-intercept form (y = mx + b), parall
1
M118 Midterm Review
Midterm: Saturday, March 5th, 9:00am-10:30am in Hodge Hall
(Kelley School of Business) room 2075.
Chapter 1
operations on sets:
union , intersection , complement 0 , Cartesian product
Venn diagrams
de Morgans laws
(A B)0 = A0 B 0
Ex+m M {oi-ler 5C1wa
PROBLEM 01: A universal set U = { a, b, c, d, e, f, g, h } has two subsets, A = { a, b, o"= f, h ), and
B = { b, c. d, g, h ). Which of the following represents the set A rt B ?
A) {b.d.h)
B) {at}
C){a.c,e,f,g}
D) (e)
E) {6.9}
N) none
\lgvgigu &_ ’
PROBLEM 01: A universal set U = { a, b. c. d, e, f, g. h ) has two subsets, A = { a, b. d. f. h }, and
B = { b, c, d, g. h}. Which of the following represents the set A n B ?
@{b,d.h}
B){a,f}
C){a.c,e,f,g} ‘
ggégig} rtﬂlb’”{bidrt‘1]
N) nohe
M118 Midterm Review
Midterm: Saturday, October 18th, 8:00am—9:30am in BE 013.
Chapter 1
o operations on sets:
union U, intersection ﬂ, complement ’, Cartesian product x
o Venn diagrams
0' de Morgan’s laws
(AUB)’ :A’nB’
(AﬂB)’mA’UB’
0 sizes of sets:
Pa
Math M118 Finite Mathematics
Suggested Practice Exercises
TEXTBOOK: Finite Mathematics: A Problem Solving Approach (copyright 2011 to present), by Watt, Hayden-McNeil
Publishing Co
To adequately prepare for all the questions on the tests and final exam, y
Take-Home Quiz #1
Math M118
Name
Class #
see Oncourse/PostEm
Score
MW12 MW130
circle one
1. Let U = cfw_1, 2, 3, 4, 5, 6, 7, 8, A = cfw_2, 4, 6, 7, and B = cfw_ 2, 4, 5, 6, 8. Find the elements in each of the sets
a.
(2)
b.
(2)
c.
BA
(2)
2. The shaded r
Take-Home Quiz #2
Math M118
Name
Class #
see Oncourse/PostEm
Score
MW12 MW130
circle one
1. In a recent survey of 70 college students, it was found that of the three weekly magazines Time, Newsweek,
and People:
30 read Time
21 read Newsweek
13 read People
Math 210, Lecture 1 Exam 1, Fall 2010
Prof: Paul Terwilliger
SOL UTmNS
Your Name (please print)
Circle your section:
Peng Zhou
T 12:05 307
R 12:05 308
T 2:25 311
R 2:25 312
NO CALCULATORS/ELECTRONIC DEVICES ALLOWED.
MAKE SURE YOU ARE SEPARATED FROM
Example: An experiment consists of rolling a red die and a green die.
(Standard dice show values of 1, 2, 3, 4, 5, or 6)
M118 Finite Mathematics
Probability, Counting, and Equally Likely Outcomes
1 / 15
Example: An experiment consists of rolling a red die
Systems with 3 or more variables & equations
If we have 3 or more equations/variables, its best to use reduction.
The goal of reduction is to get the system into triangular form.
An example of triangular form:
2x 3y + 3z
= 2
2y 4z
= 2
z
= 1
Its called tri
Ml 18
FALL 2009
QUIZ 2
NAME
6 horses are in a horse race. For the purposes of this problem, they are called A,B,C,D,E,F.
a) (10 P'rs.) In how many ways can they finish rst, second, and third?
Example: One way is to have them finish EAB (ie E wins, A
hlll8
FALL 09 QUIZ 3 NAME:
1) A vase holds 4 yellow and 2 red owers. Two owers are drawn out at random, one after the other, without
replacement.
a) (10 PTS.) Fill in the blanks on the following tree where the numbers in the right hand column indicate t
Mll8
FALL 09 Z 5 NAME:
1) A box contains 2 guavas and 1 mango. Someone selects 2 of the 3 fruit at random, one after the other,
without replacement. Let X = number of guava selected.
a) (20 PTS.) Fill in the blanks for the table showrybelow for the pro
1)
2)
Ml 18
FALL 03
QUIZ 9
PRINT NAME
SIGN NAME
SET UP FOR PROBLEMS 1 AND 2: The Old Town Canoe Company produces two types of canoes,
the Columbian and the Katahdin. The production of one Columbian canoe requires 200 hours of labor and
180 square fe
MATH M118, Spring 2016
Finite Mathematics Syllabus
Class time and place
Section 5287
Time: MWF 8:00 8:50 am
Location: Rawles Hall 100
Course web space
Oncourse will be the only web space for this course.
Instructor information
Instructor: Dr. P. Manoharan
D271, Spring 2015
EXAM I REVIEW
On the exam day, please bring to class eraser and pencils.
OFFICE HOURS: 4pm~5pm, March 31 & 2:30pm~4:30pm, April 1; HH3149
EXAM STRUCTURE: 20 multiple choice questions
TIPS FOR PREPARATION
1. Start with the knowledge point