### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Class Note for MATH 1313 with Professor Flagg at UH 2

### View Full Document

## 15

## 0

## Popular in Course

## Popular in Department

This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 15 views.

## Reviews for Class Note for MATH 1313 with Professor Flagg at UH 2

### 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: 02/06/15

13137sect7705 Page 1 of8 Math 1313 Section 75 Conditional Probability We ll start this section with an example Example 1 Two cards are drawn at random and without replacement from a wellshuffled deck of 52 playing cards a What is the probability that the first card drawn is an ace b What is the probability that the second card drawn is an ace given that the first card drawn was not an ace c What is the probability that the second card drawn is an ace given that the rst card drawn was an ace In this experiment we start with a sample space which contains 52 elements We have two events the first draw and the second draw Since there is no replacement the number in the sample space becomes smaller In parts b and c of Example 1 we learn more about the experiment which changes the sample space which changes the probabilities These are examples of conditional probability Math 1313 Class Notes 7 Section 75 Page 1 of8 13137sect7705 Page 2 of 8 We can demonstrate conditional probability using Venn diagrams Suppose we have an experiment with sample space Sand suppose Eand Fare events of the experiment We can draw a Venn diagram of this situation Now suppose we know that event Ehas occurred This gives us this picture So the probability that Foccurs given that Ehas already occurred can be expressed as nE n F nEnF nS PEnF HF m M PE 39 nS Conditional Probability of an Event If Eand Fare events of an experiment withPE 2 0 then the conditional probability that the event Fwill occur given that the event Ehas already occurred is PE nF PFlE HE Math 1313 Class Notes 7 Section 75 Page 2 of8 13137sect7705 Page 3 of 8 Example 2 Let A and Bbe events of an experiment with sample space 5 Suppose PA6 PB7 and PAnB45 Find a PAiB b PBiA Example 3 Let A and Bbe events of an experiment with sample space 5 Suppose PA48 PB 63 and PAnB 35 Find a PAiB b PBiA c PB iA d PAiB Math 1313 Class Notes 7 Section 75 Page 3 of8 13137sect7705 Page 4 of 8 Example 4 A pair of fair dice is tossed and the number on the uppermost face is observed What is the probability that the sum of the numbers falling uppermost is 6 if is it known that one of the numbers was 2 Example 5 A survey showed that 40 of all convenience store shoppers buy milk 30 buy bread and 25 buy both milk and bread a If a randomly selected shopper buys milk what is the probability that she will also buy bread b What is the probability that a randomly selected shopper buys ony bread Math 1313 Class Notes 7 Section 75 Page 4 of8 13137sect7705 Page 5 of 8 Product Rule Sometimes we know the conditional probability and are interested in finding PEnF We can solve the conditional probability formula for PEnF to get the product rule HF E PEnF PE PE FPEPFlE We will use tree diagrams for these kinds of problems to help organize the information we know The first branch of the tree is the first trial and the second branch is the second For the above formula we could illustrate the product rule by Example 6 An urn contains 5 blue marbles and 7 green marbles a Two marbles are drawn in succession and without replacement from the urn What is the probability that both marbles are green b Two marbles are drawn in succession without replacement from the urn What is the probability that the second marble is green Math 1313 Class Notes 7 Section 75 Page 5 of8 13137sect7705 Page 6 of 8 Example 7 Urn X contains 9 white marbles and 3 blue marbles Urn Y contains 5 white marbles and 6 blue marbles One of the two urns is chosen at random with equal likelihood of being chosen and then a marble is drawn from that urn What is the probability that the marble drawn is blue Example 8 A new lie detector test has been devised and needs to be tested before it can be used by the police One hundred people are selected at random and each person draws and keeps a card from a box of 100 cards Half the cards instruct the person to lie and the other half instruct the person to tell the truth The test indicated lying in 85 of those who lied and in 7 of those who did not lie What is the probability that for a randomly chosen person the person was instructed not to lie and the test did not indicate lying Math 1313 Class Notes 7 Section 75 Page 6 of8 13137sect7705 Page 7 of 8 Example 9 Mary K Cosmetics estimates that 29 of the country has seen its commercial and if a person sees its commercial there is a 13 chance that the person will not buy its products The company also claims that if a person does not see its commercial they still have a 24 chance of buying the company s products What is the probability that a randomly selected person in the country will not buy its products Independent Events Two events A and Bare independent if the outcome of one event does not depend on the outcome of the other event Test for Independence of Two Events Two events A and Bare independent if and only if PAnBPAPB This can be extended to any finite number of events Math 1313 Class Notes 7 Section 75 Page 7 of8 13137sect7705 Page 8 of 8 Example 10 Determine if the two stated events are independent The experiment is drawing a card from a wellshuffled deck of 52 playing cards a A the event of drawing a face card B the event of drawing a heart b C the event of drawing a heart D the event of drawing a club c E the event of drawing a king F the event of drawing a red card Note It is possible for the events to overlap and still be independent Many students think that mutually exclusive events and independent events mean the same thing They do not Example 11 Two events A and Bare independent PA43 and PB31 Find PAUB Math 1313 Class Notes 7 Section 75 Page 8 of8 Class 28 Review 2

### 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.