### Create a StudySoup account

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

Already have a StudySoup account? Login here

# 4.1, 4.2, 4.3 Statistics 130L

### View Full Document

## 7

## 0

## Popular in Statistics 130L

## Popular in Math

This 5 page Class Notes was uploaded by Grace Heavey on Friday October 7, 2016. The Class Notes belongs to Statistics 130L at Marist College taught by Dr. Sebesta in Fall 2016. Since its upload, it has received 7 views. For similar materials see Statistics 130L in Math at Marist College.

## Reviews for 4.1, 4.2, 4.3

### 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: 10/07/16

Intro to Statistics 4.1, 4.2 & 4.3 Probability & the Addition Rule Chapters 1, 2 & 3 cover techniques necessary for descriptive statistics. We learned how to calculate the mean, median, mode, range, and midrange. We learned about the shape of our data via frequency distributions and relative frequency distributions. We learned how to calculate how much our data varies. All of these things summarize and describe what is going on within our data. Chapter 4 is all about probability, the ﬁrst topic in inferential statistics. 4.1 & 4.2 Basics of Probability Inferential Statistics: -makes inferences (draws conclusions) about a population using data drawn from that population -statisticians collect samples from the population and draw conclusions about the entire population from the sample Rare Event Rule for Inferential Statistics: -if under a given assumption the probability of a particular event is extremely small,we can conclude the assumption was wrong Example: -IVF gender selection method:get 98 girls and 2 boys out of 100 live births 1. chance- technique is not effective 2. not chance- results didn’t occur by chance and the gender selection method works Probability: - quantifying the chance that she event will happen Event: - a collection of results from some experiment or procedure Example: -single live birth -coin ﬂip -spin a spinner Simple Event: - is an outcome or an event that cant be broken down into smaller events Example: - single birth - 3 births:not a simple event because can be broken into 3 single births ▯1 Sample Space: - all possible simple events - all possible outcomes of the experiment Example: - procedure:single birth - event:1 girl - sample space:(b,g) -procedure:toss a coin twice -event:2 heads -sample space:(tt,th,ht,hh) Notation for Probabilities: P- denotes probability A,B,and C- speciﬁc events P(A)- probability of eventA happening P(ā)- probability of all events exceptA happening( Probability Scale: 0% 50% 100% ▯2 An event is unlikely if its probability is very small .05 or less An event is unusual (extreme result) if the number of outcomes are far above or far below typical values. 9 heads in 10 coin toss- unusual Relative Frequency Approximation of Probability: -when you conduct or observe an experiment and count the number of times that EventA actually occurs P(A)= (# of times eventA occurred)/ (# of times the procedure was repeated) Example: - ﬂip a coin 75 times - count the # of heads:18 - P(heads)= 18/75= .24 - P(ā)= 57/75= .76 - P(A)+P(ā)= 1 - always adds to 1 Classical Approach to Probability (Requires Equally Likely Outcomes): - assuming that a given procedure has n different outcomes (simple events) and they are all equally likely - if eventA can happen S of n ways then P(A)= S/n= (# of ways that EventA can occur)/(# of different smile events) P(3 children of the same gender)= 2/8= .25 Sample space:bbb,ggg,bbg,bgg,gbg,ggb,bgb,gbb Subjective Probabilities: -guestamates -P(A) is estimate by using knowledge of relevant circumstances Example: P(dying in a plane crash) thousands of ﬂights daily - rarely a fatal plane crash 1 in 10 million Law of Large Numbers: -the more times a procedure is repeated the closer the relative frequency probability tends to approach the actual probability ▯3 4.3 Addition Rule: The addition rule is a tool for ﬁnding the probability of event or event or Notation: P(A or B) - in a single trail the probability of eventA OR event B OR both will happen compound event:an event combining 2 or more simple events Formal Addition Rule: P(A or B) = P(A) + P(B) - P(A and B) Example: - roll a 6 sided die - P(2 or 5) = 1/6 + 1/6 = 1/3 - P(2)=1/6 - P(5)=1/6 -spinner divided into 4 equal colors:red,blue,green,yellow -P(R or B)= 1/4 + 1/4= 1/2 - P(R)= 1/4 - P(B)= 1/4 Intuitive Addition Rule: -To ﬁnd the P(A or B) ﬁnd the sum of the number of ways eventA can occur and the number of times event B can occur and add them in such a way that each outcome is only counted once - P(A orB)= sum of P(A) and P(B) / total # of outcomes in the sample space Example: -P(king or club) = 4/52 + 13/52 - 1/52 = 16/52= 4/13=.3077 P(king) = 4/52 P(king of clubs) = 1/52 P(club)= 13/52 round to 4 digits disjoint: -mutually exclusive -eventA and event B can not happen at the same time ▯4 Example: disjoint (a) (b) not disjoint (a()b) Complementary Events & the Addition Rule: P(A or ā) = 1 P(A) + P(ā) = 1 P(A) = 1-P(ā) P(ā)+ 1 -P(A) Example: roll a 6 sided dice P(3) =1/6 P(not 3)= 5/6 P(A) = .76 P(ā)= 1 - .76 = .24 ▯5

### 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

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

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

#### "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."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION 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 support@studysoup.com

#### STUDYSOUP REFUND POLICY

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: support@studysoup.com

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 support@studysoup.com

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.