# Connexions

You are here: Home » Content » Collaborative Statistics » Venn Diagrams (optional)

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### In these lenses

• Lucy Van Pelt

This collection is included inLens: Lucy's Lens
By: Tahiya Marome

"Part of the Books featured on Community College Open Textbook Project"

Click the "Lucy Van Pelt" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Bio 502 at CSUDH

This collection is included inLens: Bio 502
By: Terrence McGlynn

"This is the course textbook for Biology 502 at CSU Dominguez Hills"

Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

# Venn Diagrams (optional)

Summary: This module introduces Venn diagrams as a method for solving some probability problems. This module is included in the Elementary Statistics textbook/collection as an optional lesson.

A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

## Example 1

Suppose an experiment has the outcomes 1, 2, 3, ... , 12 where each outcome has an equal chance of occurring. Let event A = {1, 2, 3, 4, 5, 6}A = {1, 2, 3, 4, 5, 6} and event B = {6, 7, 8, 9}B = {6, 7, 8, 9}. Then A AND B = {6}A AND B = {6} and A OR B = {1, 2, 3, 4, 5, 6, 7, 8, 9}A OR B = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The Venn diagram is as follows:

## Example 2

Flip 2 fair coins. Let AA = tails on the first coin. Let BB = tails on the second coin. Then A = {TT, TH} A={TT,TH} and B = {TT, HT}B={TT,HT}. Therefore, A AND B = {TT}A AND B = {TT}. A OR B = {TH, TT, HT}A OR B = {TH,TT,HT}.

The sample space when you flip two fair coins is S = {HH, HT, TH, TT}S ={HH,HT, TH,TT}. The outcome HHHH is in neither AA nor BB. The Venn diagram is as follows:

## Example 3

Forty percent of the students at a local college belong to a club and 50% work part time. Five percent of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let CC = student belongs to a club and PT PT = student works part time.

If a student is selected at random find

• The probability that the student belongs to a club. P(C) = 0.40P(C)= 0.40.
• The probability that the student works part time. P(PT) = 0.50P(PT)=0.50.
• The probability that the student belongs to a club AND works part time. P(C AND PT) = 0.05P(C AND PT)= 0.05.
• The probability that the student belongs to a club given that the student works part time.
P(C|PT)  =  P(C AND PT) P(PT)  =  0.05 0.50  =  0.1 P(C|PT) =  P(C AND PT) P(PT)  =  0.05 0.50  = 0.1
(1)
• The probability that the student belongs to a club OR works part time.
P(C OR PT) = P(C) + P(PT) - P(C AND PT) = 0.40 + 0.50 - 0.05 = 0.85 P(C OR PT) = P(C) + P(PT) - P(C AND PT) = 0.40 + 0.50 - 0.05 = 0.85
(2)

## Glossary

Venn Diagram:
The visual representation of a sample space and events in the form of circles or ovals showing their intersections.

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks