New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

MATH-M 018 Exam 1 Study Guide

by: Abigail Dolbeer

MATH-M 018 Exam 1 Study Guide MATH-M 18

Marketplace > Indiana University > Mathematics > MATH-M 18 > MATH M 018 Exam 1 Study Guide
Abigail Dolbeer

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

This goes over the material for exam 1
Basic Algebra For Finite Math
Linda McKinley
Study Guide
Math, Probability, Permutations, Combinations
50 ?




Popular in Basic Algebra For Finite Math

Popular in Mathematics

This 4 page Study Guide was uploaded by Abigail Dolbeer on Wednesday September 7, 2016. The Study Guide belongs to MATH-M 18 at Indiana University taught by Linda McKinley in Summer 2016. Since its upload, it has received 10 views. For similar materials see Basic Algebra For Finite Math in Mathematics at Indiana University.


Reviews for MATH-M 018 Exam 1 Study Guide


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/07/16
MATH-M 018 Exam 1 Study Guide Ch 1: Sets Sets: a collection of objects (elements) Sets are generally noted by a capital letter The order in which the elements appear in the set is not important Notation of sets: list each element, separated by a comma, surrounded by braces Example: {1, 3, 5, 7} or {1, 3, 5, …} Finite set Infinite set ∈ : is an element of ∉ : is not an element of A= {1, 4, 8, 10} so 4 ∈ set A and 5 ∉ set A Universal Set: a set that contains everything (that is relevant to the question) Equality: two sets are equal if they have precisely the same numbers Set A=B were A is the set whose numbers Are the first four positive whole numbers B= {1, 2, 3, 4} Empty Set: a set with no elements; ∅ symbolizes empty set Subset: when a set is defined, a subset can be formed with pieces of that set Ex: A is a subset of B where A= {1,3,4} and B= {1,4,3,2} ⊂ is a subset of ⊄ is not a subset Set Builder Notation: describes a set by saying what properties the set has {x | x > 0} = the set of all xs such that x is greater than 0 All x X is greater than 0 The set of Such that Complements: complements of a set contain every element not in that set The complement of S is denoted by S’ (pronounced S prime) S’ contains every element not in S Set Operations: Intersection: The intersection A ∩ B is the set that contains elements of A that also belong to B Union: the set of all distinct elements in the collection Venn Diagrams: a way of picturing an expression involving one or more sets Steps: 1. Draw a rectangle which represents the universal set. 2. Inside the rectangle, circles are used to represent various sets in the universe. 3. Circles are always overlapping to allow for the possibility that the sets may have elements in common. • Note that emptiness is a possibility Using Venn Diagrams in Problem Solving: 1. Define the steps 2. Enter the given information into a venn diagram Ch. 2 Probability and Counting Experiments and events: An experiment is any situation whose outcome is uncertain and can be thought of as an experiment. Experiments consist of finitely many outcomes. Probability theory is the field of mathematics that was developed to answer probability questions. Sample space of an experiment is the set of all outcomes of the experiment. A sample space is often denoted “S”. Complementary events: Probability: likelihood of something happening If the sample space for an experiment consists of n equally likely outcomes, then the probability we assign to each of the outcomes is 1/n. Suppose that E is an event in a sample space with equally likely outcomes. Then, the probability that event E will occur, denoted Pr(E), is: Pr(E)= n(E)/n(S) The relationship between the number of outcomes in an event & the number of outcomes in its complement is given by: N(E) + N(E’) = n(S) Relationship between the probabilities of an event and its complement: N(E)/n(S) + n(E’)/n(S) = n(S)/n(S) or Pr(E) + Pr(E’) = 1 The Multiplication Principle: states that if a multi-stage experiment has n1, outcomes at stage 1, n2 outcomes at stage 2 (regardless of the result of stage 1), n3 outcomes at stage 3 (regardless of the results of the first two stages), and so on until nk outcomes at stage k (regardless of the results of the previous stages) then the experiment has n1 x n2 x n3 x… x nk outcomes. • One can think of the multiplication principle as “filling slots”. Each slot represents a stage of the experiment, and the number you place in the slot is the number of outcomes at that stage. • Suppose that E is an event in a sample space with equally likely outcomes. Then the probability that event E will occur, denoted Pr(E) is: Pr(E)= n(e)/n(s) Permutations: an ordering of some set of elements If n is a positive whole number, the notation n! is read “n factorial” and stands for the product: n x (n-1) x (n-2) x (n-3) . . . 3 x 2x 1 If n is a positive whole number, then there are n! ways to order n different things Combinations: Combinations are different than permutations because combinations cannot be counted directly by “filling slots” because the multiplication principles always counts all possible orders Permutations: ordered lists, ordering, arrangement Combinations: selection, collection, (sub)sets The formula for calculating C(n,r) 1. The number of ways to order r things is r! 2. The number of ways to select and arrange r things from n is: P(n,r)= n!/(n-1)! The number of ways to select and order r things from n is the number of ways to select r things from n times is the number of ways to order them: P(n,r) = C(n,r) x r! The number of ways to select a set of r things from n is called the number of combinations of n things taken r at a time and is denoted C(n , r) where: C(n , r) = n!/r!(n-r)!


Buy Material

Are you sure you want to buy this material for

50 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.