'73.
'74.
1'5.
'76.
77.
After you have read this section. you
should be able to:
2 Compute empirical probability.
100% or 17
l
1
L50% 0'2,
magma
I used the formula for RC, to determine how many four-letter
passwords with no repeated letters can be forme
. WHAT AM |
SUPPOSED TO LEARN?
|liAlter you have read this sectionl you
should be able to:
I Find the probability that an
event will not occur.
2 Find the probability of one event
or a second event occurring.
3 Understand and use odds.
Find the probabilit
SECTION 2.2 Subsets 6|
Subsets
MATH TATTOOS. WHO KNEW? EMERGING
from their often unsavory reputation of the
recent past, tattoos have gained increasing
prominence as a form of body art and self-
expression. A Harris poll conducted in 2012
estimated that 4
694 CHAPTER I l Counting Methods and ProbabilityTheory
29. The statement in the last frame of this cartoon is highly unlikely because there are 2048 possible sets of answers on an eleven-item
true/false test.
Peanuts I968 PeanuosWorl- imbued by Universa
96 CHAPTER2 SetTheory
WHAT AM |
SUPPOSED TO LEARN?
After you have read this section, you
should be able to:
I UseVenn diagrams to visualize a
surveys results.
2 Use survey results to complete
Venn diagrams and answer
questions about the survey.
FIGU RE
MAT 142 Course Syllabus | Fall 2015 B
MAT 142: College Mathematics
Fall 2015 oCourse Syllabus
Instructor: insert name
Office: insert office
E-mail: insert email
Office Hours:
Insert office hours
Course Information
Course Description
Welcome to MAT 142! Th
Probability Problem Set
Name: _
1. We are flipping three coins. Outcomes are represented by strings of Hs and Ts. For example, HHH is one
outcome.
A. How many elements are in the sample space?
B. What is the probability of getting two heads?
C. What is th
84 CHAPTER). SetTheory
Set Operations and Venn Diagrams
with Three Sets
SHOULD YOUR BLOOD TYPE
WHAT AM I
determine what on eat? The
7 y
SUPPOSED TO LEARN. blood-type diet, developed by ,
naturopathic physician Peter
DAdamo, is based on the theory
Afte
76 CHAPTER2 SetTheory
We can nd the union of set A and set B by listing the elements of set A.
Then, we include any elements of set B that have not already been listed. Enclose
all elements that are listed with braces. This shows that the union of two set
48 CHAPTER). SetTheory
Basic Set Concepts
WE TEND TO PLACE THINGS IN
categories, which allows us to order
WHAT AM I and structure the world.For example,
SUPPOSED TO LEARN? to which populations do you
After you have read this section,you belong? DO you cat
SECTION I |.7 Events Involving And: Conditional Probability 737
98. Explain how to nd the odds in favor of an event if you 102. The probability of selecting a king or a heart from a deck of
know the probability that the event will occur. 52 cards is the s
54 CHAPTER). SetTheory
5 Determine 21 sets cardinal number
EXAMPLE 7 Representing Sets ofNatuml Numbers
Express each of the following sets using the roster method:
a. cfw_xleN and x5 100 b. cfw_xIxEN and 70$x< 100.
SOLUTION
a. cfw_x l x EN and x s 100 r
702 CHAPTER I l Counting Methods and ProbabilityTheory
Critical Thinking Exercises 69. Six horses are entered in a race. If two horses are tied for rst
place, and there are no ties among the other four horses, in
Make Sense? In Exercises 6462determine whe
70 CHAPTER 2
SetTheory
Writing in Mathematics
99.
100.
101.
102.
103.
104.
Explain what is meant by a subset.
What is the difference between a subset and a proper subset?
Explain why the empty set is a subset of every set.
Describe the difference between
688 CHAPTER I l Counting Methods and ProbabilityTheory
WHAT AM |
SUPPOSED TO LEARN?
After you have read this section,you
should be able to:
I Use the Fundamental Counting
Principle to determine the
number of possible outcomes in
a given situation.
I Use
SECTION |.8 ExpectedValue 749
Expected Value
WOULD YOU BE WILLING TO SPEND $50 A YEAR
for an insurance policy that pays $200,000 if you
become too ill to continue your education? It is
unlikely that this will occur. Insurance companies
make money by compe
742 CHAPTER I l Counting Methods and ProbabilityTheory
The multiplication rule for dependent events can be extended to cover three or
more dependent events. For example, in the case of three such events,
P(A and B and C)
= P(A) - P(B given that A occurred
Probability: Probability Rules
Directions:
1. Solve the following problems. Write your solutions and explanations on
your own paper between standard notebook size (8x10.5) and standard
typing paper size (8.5x11). You must use pencil (no pens).
2. Show you
MATHEMATICS
All students are required to take a minimum of one math course that satisfies the general studies
requirement for mathematics (MA). The appropriate math course will be based on the major(s) you want
to pursue, placement score, and ability leve
MAT 275 - MATLAB #5
% Lab 5 Jose Cabrera - MAT 275 Lab
% Solution 1
The curve in blue represents the equation y = y(t). Since according to the initial conditions in
LAB05ex1 the mass in the spring-mass system is displaced from its zero position. Clearly,
MATLAB sessions: Laboratory 3
MAT 275 Laboratory 3
Numerical Solutions by Euler and Improved Euler Methods
(scalar equations)
In this session we look at basic numerical methods to help us understand the fundamentals of numerical
approximations. Our object
MAT 275 MATLAB LAB 4
SLN: 26141
% Lab 4 Jose Cabrera - MAT 275 Lab
% Solution 1.A
function LAB04ex1
t0 = 0;
tf = 50;
y0 = [-0.5;0.5]; % Specify the initial conditions here
[t,Y] = ode45(@f,[t0,tf],y0);
% Get the solution for position
y = Y(:,1);
% Get the
MATLAB sessions: Laboratory 5
MAT 275 Laboratory 5
The Mass-Spring System
In this laboratory we will examine harmonic oscillation. We will model the motion of a mass-spring
system with differential equations.
Our objectives are as follows:
1. Determine th
% Lab 2 - Your Name - MAT 275 Lab
% Example code
% Example 1
% NOTE: Delete examples before submission.
A = [1 0; 0 -1]
A = [1, 0; 0, -1]
% NOTE: The two matrices above are the same. We can separate columns with
% commas OR spaces, and separate rows with
Dated April 18th 2017
To, Ms. Kim
From, Ali
Article Review 6
Psychological Therapies
Therapy
Therapy is also called psychotherapy or counseling, is the process of meeting with a therapist to
resolve problematic behaviors, beliefs, feelings, relationship i
MATH 242 Written HW3 Due Thursday, April 26
PLEASE'SUBMIT PDF FILE ON BLACKBOARD WITH YOUR SOLLUTION (WRITTEN OR
TYPED) SHOW ALL YOUR WORK! GOOD LUCK! NAME:
NOTE: There are two problems in this HW. Dont forget the one on page 2!
AkrIII
1; (10 pts.) Vector
SOLUTION
MATH 242 Written HW2 Due Tuesday, April 4
PLEASE SUBMIT THESE TWO PROBLEMS IN CLASS (NOT VIA EMAIL). SHOW ALL
YOUR WORK! GOOD LUCK! NAME:
3 5 9
1. (10 pts.) Determine whether the vectors 11 = 1 , 43' = 4 , u') : 14 are linearly
"2 6 22
dependen
For all x, there exists y. Proof Writing
The basic logical structure of a for all , there exists such that (, ) proof is like this:
Suppose is arbitrary. Let = ( some function of that comes seemingly out of
nowhere). Then (show how with this choice of y,
Examples of Theorems with Proofs
Theorem 1: Every even number can be written as the sum of two odd numbers whose difference is at
most two.
Theorem 2: For any natural number , there is an odd integer such that 2 < < ( + 1)2 .
Theorem 3: For every real num