prob questions

7/28/2019 PROB QUESTIONS

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ProbabilityOverview

In this section we will cover:

Expressing probabilities

GMAT Probability Rule #1GMAT Probability Rule #2

GMAT Probability Rule #3GMAT Probability Rule #4

Probability

You may encounter questions on the GMAT that ask the probability of

an event occuring. For instance:

Sara rolls two fair, six-sided dice. What is the probability she will

roll two 6s?

Roland flip two fair coins. What is the probability that neither of

the coins will land on tails?

A bag contains six blue marbles and six red marbles. If Teresa

randomly chooses a marble from the bag, what is the probability

that the marble is blue?

All of these problems are probability problems. Probability is a

measure of the likelihood of an event occurring.Expressing Probability

The probability of an event occurring is expressed as a

number between 0 and 1. A probability of 0 means theevent can never happen. A probability of 1 means the

event is certain to happen.

You may see probability express on the GMAT in terms of

a percent, a decimal, or a fraction. For instance, theprobability of a fair coin landing on tails can be expressed

as

Fraction 1/2

Decimal .5

Percent 50


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%

Sometimes you may see notation similar to that below:

P(A) = 1/2

This means that the probability of an event A is 1/2.

Probability Rules

There are four probability rules you need to memorize in order tomaster GMAT probability questions:

1. The probability of an event A occurring is the number ofoutcomes that result in A divided by the total number of

possible outcomes.

2. The probability of an event occurring plus the probability of

the event not occurring equals 1.

3. The probability of event A AND event B occurring is theprobability of event A times the probability of event B given

that event A has already occurred.

4. The probability of event A OR event B occurring is theprobability of event A occurring plus the probability of event Boccurring minus the probability of both events occurring.

The probability of an event A occurring is the number of

outcomes that result in A divided by the total number ofpossible outcomes.

Example: Raphael tosses a fair coin. What is the probability the

coin will come up heads?

Probability of heads = [heads]/[heads, tails]Probability of heads = 1/2

Example: Tom rolls a fair die. What is the probability that thedie will roll an even number?

Probability of even number = [2, 4, 6]/[1, 2, 3, 4, 5, 6]


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Probability of even number = 3/6Probability of even number =

Rule #2

The probability of an event occurring plus the probability of theevent not occurring equals 1.

In other words, we can say with 100% certainty that an event willeither occur or not occur. For instance, the probability of a fair, six-

sided die rolling a 4 is 1/6. The probability of the die not landing on 4is (1 - 1/6) or 5/6. 1/6 + 5/6 = 1.

This concept can be very helpful on the GMAT. Sometimes it is easierto determine the probability of an event not occurring than

determining the probability of an event occurring. Once your know theprobability of an event not occurring, you can subtract the probability

from 1 to find the probability of an event occurring.

Rule #3

The probability of event A AND event B occurring is the

probability of event A times the probability of event B giventhat event A has already occurred.

Example: Joseph rolls two fair, six-sided die. What is theprobability that both die will roll a 6?

Probability of 1st die coming up 6: 1/6

Probability of 2nd die coming up 6: 1/6

Probability of both die coming up 6: (1/6) * (1/6)Probability of both die coming up 6: 1/36

Example: A bag contains three blue marbles and three red

marbles. If two marbles are drawn randomly from the bag,

what is the probability that they are both blue?

This problem is a dependent probability. Two events are said to bedependent events if the outcome of one event affects the outcome of

the other event. The probability of drawing the second marble dependson the outcome of the first marble. If the first marble is red, there is

no possibility of drawing two blue marbles. Thus, the probability of

drawing a second blue marble is calculated after the first blue marblehas been drawn.


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Probability of drawing blue on first draw: 3/6

If a blue is drawn on the first draw, there are three red marbles and

two blue marbles remaining in the bag.

Probability of drawing blue on second draw (given that first was blue):

2/5

Probability of drawing two blue: (3/6) * (2/5)

Probability of drawing two blue: 6/30Probability of drawing two blue: 1/5

Rule #4

The probability of event A OR event B occurring is theprobability of event A occurring plus the probability of event B

occurring minus the probability of both events occurring.

Example: Charles rolls a fair, six-sided die. What is the

probability of Charles rolling a 2 or a 4?

Probability of 2: 1/6Probability of 4: 1/6

Probability of a 2 or 4: 1/6 + 1/6

Probability of a 2 or 4: 2/6

Probability of a 2 or 4: 1/3

In the previous problem, the events were mutually exclusive.

Mutually exclusive means that the events cannot occur together. There

is no way to roll a 2 and a 4 at the same time. The events in thefollowing problem are NOT mutually exclusive.

Example: Of the 100 students at a certain school, 30 students

are taking a chemistry class, 40 students are taking a physics

class, and 20 students are taking both a physics and a

chemistry class. If a student is chosen at random from theschool, what is the probability that he or she is taking a physicsor a chemistry class?

Probability of selecting a student taking a chemistry course: 30/100Probability of selecting a student taking a physics class: 40/100

Probability of selecting a student taking both classes: 20/100Probability of a selecting a student taking chemistry OR a student


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taking physics: 30/100 + 40/100 - 20/100 = 50/100 or 1/2

There are 9 beads in a bag. 3 beads are red, 3

beads are blue, and 3 beads are black. If twobeads are chosen at random, what is the

probability that they are both blue?

A. 1/81

B. 1/12

C. 2/9

D. 1/3

E. 1/4

A letter is randomly selected from the wordMississippi. What is the probability that the letterwill be an s?

A. 1/11

B. 3/10

C. 4/11

D. 1/4

E. 1/3

A certain deck of cards contains 2 blue cards, 2red cards, 2 yellow cards, and 2 green cards. If

two cards are randomly drawn from the deck,what is the probability that they will both are not

blue?

A. 15/28

B. 1/4

C. 9/16

D. 1/32

E. 1/16

A fair coin is tossed, and a fair six-sided die is


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rolled. What is the probability that the coin comeup heads and the die will come up 1 or 2?

A. 1/2

B. 1/4

C. 1/6

D. 1/12

E. 1/3

A bag of 10 marbles contains 3 red marbles and7 blue marbles. If two marbles are selected at

random, what is the probability that at least onemarble is blue?

A. 21/50

B. 3/13

C. 47/50

D. 14/15

E. 1/5

A fair, six-sided die is rolled. What is theprobability that the number will be odd?

A. 1/4

B. 1/2

C. 1/3

D. 1/6

E. 1/5A letter is randomly select from the wordstudious. What is the probability that the

letter be a U?

A. 1/8

B. 1/4


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C. 1/3

D. 1/2

E. 3/8

A bag contains 2 red beads, 2 blue beads, and 2

green beads. Sara randomly draws a bead from

the bag, and then Victor randomly draws a beadfrom the bag. What is the probability that Sara

will draw a red marble and Victor will draw ablue marble?

A. 2/13

B. 1/5

C. 1/3

D. 1/10

E. 2/15

If two fair, six-sided dice are rolled, what is the

probability that the sum of the numbers will be5?

A. 1/6B. 1/4

C. 1/36

D. 1/18

E. 1/9

If four fair coins are tossed, what is the

probability of all four coming up heads?

A. 1/4

B. 1/6

C. 1/8

D. 1/16

E. 1/32


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The probability that a certain event will occur is

5/9. What is the probability that the event willNOT occur?

A. 5/9

B. 4/9

C. 2/9

D. 1/4

E. 1/2

A certain bag contains red, blue, yellow, and

green marbles. If a marble is randomly drawn

from the bag, the probability of drawing a bluemarble is .2, the probability of drawing a red

marble is .3, and the probability of drawing ayellow marble is .1. What is the probability of

drawing a green marble?

A. .5

B. .6

C. .2

D. .4

E. .3

A bag contains 3 red marbles, 3 blue marbles,and 3 green marbles. If a marble is randomly

drawn from the bag and a fair, six-sided die is

tossed, what is the probability of obtaining a redmarble and a 6?

A. 1/15

B. 1/6

C. 1/3

D. 1/4

E. 1/18


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A fair, six-sided die is rolled. What is the

probability of obtaining a 3 or an odd number?

A. 1/6

B. 1/5

C. 1/4

D. 2/3

E. 1/2

At a certain business school, 400 students aremembers of the sailing club, the wine club, or

both. If 200 students are members of the wine

club and 50 students are members of both clubs,what is the probability that a student chosen at

random is a member of the sailing club?

A. 1/2

B. 5/8

C. 1/4

D. 3/8

E. 3/5

A bag contains six marbles: two red, two blue,and two green. If two marbles are drawn at

random, what is the probability that they are thesame color?

A. 1/3

B. 1/2

C. 1/8

D. 1/4

E. 1/5

There are five students in a study group: two

finance majors and three accounting majors. If


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two students are chosen at random, what is theprobability that they are both accounting

students?

A. 3/10B. 2/5

C. 1/5

D. 3/5

E. 4/5

Seven beads are in a bag: three blue, two red,and two green. If three beads are randomly

drawn from the bag, what is the probability that

they are not all blue?

A. 5/7

B. 23/24

C. 6/7

D. 34/35

E. 8/13

A bag has six red marbles and six blue marbles.If two marbles are drawn randomly from the

bag, what is the probability that they will bothbe red?

A. 1/2

B. 11/12

C. 5/12

D. 5/22

E. 1/3

Webdynpro Java( admin and development )

1.Introduction to SAP product strategynetweaver Architecture


11/23

Enterprise Portal Architecture, WAS architecture

Transition from desktop to desktop

Iviews, pages, roles, workset, users, groupsCustomizing portal

Connection to SAPR/3, SAP BW, SAP CRM

Connection to ORACLE,Yahoo, google services.Various Iviews

SAP URL Iview, SAP Transaction Iview

SAP BSP Iview, SAP BW Report IviewSAP Webdynpro Iview, Webservice Iview

JDBC stored procedure Iview, Portal Activity report Iview

Single-Sign On, SAP logon tickets

Portal PersonalizationPortal Internationalization

Transporting/Import/Export EPA Files

Portal development kit

SAP R/3 Fundamentals, SAP BW FundamentalsRemote function module/RFC/BAPI

Transaction codes, internal tablesWAS Java Admin Tools

Config Tool

Visual J2ee Admin ToolSDM GUI, System Analyzer

Security-user management (users, groups)

System Landscape

SLD configurationJCO destinations

NWDI configuration

DTR TracksCMS Runtime Systems

CBS - Ready-to use Libraries

SLD Information of SystemsESS/MSS business packages

Introduction of ESS/MSS

Configuration of ESS/MSS

Customization of ESS/MSS dcsInstallation of Portal

Pre-Install, Install, Post-Install

Visual Composer Setup

Knowledge management and collaboration

Business objectives of KM

KM platform: architecture overview, real time collaboration


12/23

Repositories, ACL, Trex components, crawler

Permissions

Versioning in KM, Publishing documentsKM Iviews:

KM document Iview, subscription, Approval

KM navigation IviewKM quickpoll admin Iview

KM quickpoll Iview

KM XML forms builder IviewKM UPLOAD Iview

KM discussions Iview

KMC asynchronous collaboration

Versioning, permissions, lifetime in KMCollaboration launch pad,

Creating WEB Folder and using them in KM Repository

Creating and maintaining collaboration rooms

Email integrationExample based TAXONAMY

Query based TAXONAMY

Webdynpro Java (development):

Webdynpro introduction, NWDSMVC architecture\

Webdynpro user interface elements

Table, image, DDBI, DDBK, itemlistbox, progress indicator etcFile upload, file download

Value selectors

SVS, EVS, OVS

Validations (Range, length, datatype)Local dictionary, simple type, structures, java native types

Component object model

Business graphicsAdobe Interactive forms

Microsoft office integration

Data binding, table binding, structure binding.

Context mapping, model binding, views, view setsVarious controllers

Error handling, message editor, messages

Webdynpro internationlizationDebugging techniques in webdynpro

Models, developing custom BAPIs/RFCs

Using calculated attributes, supply functionsTypes of models


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Adaptive RFC model

Webservice model

Java bean modelCreating webdynpro application as Iview

SLD config, JCO destinations

Popup, external, confirmation diaglog windowsWebdynpro security programming

Application and URL parameters

Webdynpro service and Helper classesDynamic programming

Fine tuning and performance issues

Reuse concepts of development components

Reading data and values from properties files.

VISUAL COMPOSER

Visual composer setupVC architecture

Forms, tables, image managerValue helps

Formulas

Visual composer internationalizationData intensive operations

Searching, sorting, filtering, aggregates

Entry lists:

Static, dynamicData services:

BAPIs/RFCs

WebservicesBI queries

BASIS

WDA and WDJ BASICS

Webdynpro Java( a

WDA and WDJ BASICS


1.Introduction to SAP product strategynetweaver Architecture

Enterprise Portal Architecture, WAS architecture

Transition from desktop to desktopIviews, pages, roles, workset, users, groups

Customizing portal

Connection to SAPR/3, SAP BW, SAP CRM

Connection to ORACLE,Yahoo, google services.


14/23

Various Iviews

SAP URL Iview, SAP Transaction Iview

SAP BSP Iview, SAP BW Report IviewSAP Webdynpro Iview, Webservice Iview

JDBC stored procedure Iview, Portal Activity report Iview

Single-Sign On, SAP logon ticketsPortal Personalization

Portal Internationalization

Transporting/Import/Export EPA FilesPortal development kit

SAP R/3 Fundamentals, SAP BW Fundamentals

Remote function module/RFC/BAPI

Transaction codes, internal tablesWAS Java Admin Tools

Config Tool

Visual J2ee Admin Tool

SDM GUI, System AnalyzerSecurity-user management (users, groups)

System LandscapeSLD configuration

JCO destinations

NWDI configurationDTR Tracks

CMS Runtime Systems




Configuration of ESS/MSSCustomization of ESS/MSS dcs

Installation of Portal

Pre-Install, Install, Post-InstallVisual Composer Setup


Business objectives of KMKM platform: architecture overview, real time collaboration

Repositories, ACL, Trex components, crawler

PermissionsVersioning in KM, Publishing documents

KM Iviews:

KM document Iview, subscription, Approval

KM navigation Iview


15/23

KM quickpoll admin Iview

KM quickpoll Iview



KMC asynchronous collaborationVersioning, permissions, lifetime in KM

Collaboration launch pad,

Creating WEB Folder and using them in KM RepositoryCreating and maintaining collaboration rooms

Email integration

Example based TAXONAMY






Value selectors

SVS, EVS, OVSValidations (Range, length, datatype)

Local dictionary, simple type, structures, java native types

Component object modelBusiness graphicsAdobe Interactive forms


Data binding, table binding, structure binding.Context mapping, model binding, views, view sets

Various controllers

Error handling, message editor, messagesWebdynpro internationlization

Debugging techniques in webdynpro


Using calculated attributes, supply functionsTypes of models

Adaptive RFC model

Webservice modelJava bean model

Creating webdynpro application as Iview

SLD config, JCO destinationsPopup, external, confirmation diaglog windows


16/23

Webdynpro security programming




Reuse concepts of development componentsReading data and values from properties files.

VISUAL COMPOSER

Visual composer setup

VC architecture


Formulas

Visual composer internationalization

Data intensive operationsSearching, sorting, filtering, aggregates

Entry lists:Static, dynamic

Data services:

BAPIs/RFCsWebservices

BI queries

Web Dynpro for ABAP | webdynpro samples

and tutorialWebDynpro for ABAP (WD4A, WDA) is the SAP standard UI ( user interface) technology for

developing Web applications in the ABAP language. It consists of a runtime environment and

a graphical development environment with special Web Dynpro tools that are integrated in

the ABAP Workbench (SE80).

Web Dynpro offers the following advantages for application developers:

The use of declarative and graphical tools significantly reduces the

implementation effort

Web Dynpro supports a structured design process

Strict separation between layout and business data

Reuse and better maintainability by using components

The layout and navigation is easily changed using the Web Dynpro tools


17/23

Stateful applications are supported that is, if the page is changed and the

required data remains intact so that you can access it at any time throughout the entire

application context.

Note that stateless applications are not possible.

Automatic data transport using data binding

Automatic input check

User interface accessibility is supported

Full integration in the reliable ABAP development environment

dmin and development )

1.Introduction to SAP product strategy

netweaver ArchitectureEnterprise Portal Architecture, WAS architecture

Transition from desktop to desktopIviews, pages, roles, workset, users, groups

Customizing portal

Connection to SAPR/3, SAP BW, SAP CRMConnection to ORACLE,Yahoo, google services.

Various Iviews

SAP URL Iview, SAP Transaction IviewSAP BSP Iview, SAP BW Report Iview

SAP Webdynpro Iview, Webservice Iview

JDBC stored procedure Iview, Portal Activity report IviewSingle-Sign On, SAP logon ticketsPortal Personalization

Portal Internationalization

Transporting/Import/Export EPA FilesPortal development kit

SAP R/3 Fundamentals, SAP BW Fundamentals

Remote function module/RFC/BAPITransaction codes, internal tables

WAS Java Admin Tools

Config Tool

Visual J2ee Admin ToolSDM GUI, System Analyzer

Security-user management (users, groups)

System LandscapeSLD configuration

JCO destinations

NWDI configurationDTR Tracks


18/23

CMS Runtime Systems




Configuration of ESS/MSSCustomization of ESS/MSS dcs


Pre-Install, Install, Post-InstallVisual Composer Setup



KM platform: architecture overview, real time collaborationRepositories, ACL, Trex components, crawler

PermissionsVersioning in KM, Publishing documents

KM Iviews:

KM document Iview, subscription, ApprovalKM navigation Iview


KM quickpoll Iview



KMC asynchronous collaborationVersioning, permissions, lifetime in KM

Collaboration launch pad,

Creating WEB Folder and using them in KM RepositoryCreating and maintaining collaboration rooms

Email integration

Example based TAXONAMY







19/23

Value selectors

SVS, EVS, OVS

Validations (Range, length, datatype)Local dictionary, simple type, structures, java native types

Component object model

Business graphicsAdobe Interactive forms


Data binding, table binding, structure binding.Context mapping, model binding, views, view sets

Various controllers

Error handling, message editor, messages

Webdynpro internationlizationDebugging techniques in webdynpro


Using calculated attributes, supply functions

Types of modelsAdaptive RFC model

Webservice modelJava bean model

Creating webdynpro application as Iview

SLD config, JCO destinationsPopup, external, confirmation diaglog windows





Reuse concepts of development componentsReading data and values from properties files.

VISUAL COMPOSER

Visual composer setup

VC architecture


Formulas

Visual composer internationalizationData intensive operations

Searching, sorting, filtering, aggregates

Entry lists:Static, dynamic

Data services:

BAPIs/RFCs

Webservices


20/23

BI queries


1.Introduction to SAP product strategy

netweaver ArchitectureEnterprise Portal Architecture, WAS architecture

Transition from desktop to desktop

Iviews, pages, roles, workset, users, groups

Customizing portalConnection to SAPR/3, SAP BW, SAP CRM

Connection to ORACLE,Yahoo, google services.

Various Iviews

SAP URL Iview, SAP Transaction IviewSAP BSP Iview, SAP BW Report Iview

SAP Webdynpro Iview, Webservice IviewJDBC stored procedure Iview, Portal Activity report Iview

Single-Sign On, SAP logon tickets

Portal PersonalizationPortal Internationalization

Transporting/Import/Export EPA Files

Portal development kit

SAP R/3 Fundamentals, SAP BW FundamentalsRemote function module/RFC/BAPI

Transaction codes, internal tables

WAS Java Admin ToolsConfig Tool

Visual J2ee Admin Tool

SDM GUI, System AnalyzerSecurity-user management (users, groups)

System Landscape

SLD configuration

JCO destinationsNWDI configuration

DTR Tracks

CMS Runtime SystemsCBS - Ready-to use Libraries

SLD Information of Systems

ESS/MSS business packagesIntroduction of ESS/MSS

Configuration of ESS/MSS

Customization of ESS/MSS dcs



21/23

Pre-Install, Install, Post-Install

Visual Composer Setup



KM platform: architecture overview, real time collaborationRepositories, ACL, Trex components, crawler

Permissions

Versioning in KM, Publishing documents

KM Iviews:KM document Iview, subscription, Approval

KM navigation Iview


KM quickpoll IviewKM XML forms builder Iview

KM UPLOAD IviewKM discussions Iview

KMC asynchronous collaboration

Versioning, permissions, lifetime in KMCollaboration launch pad,

Creating WEB Folder and using them in KM Repository

Creating and maintaining collaboration rooms

Email integrationExample based TAXONAMY



Webdynpro introduction, NWDS

MVC architecture\Webdynpro user interface elements

Table, image, DDBI, DDBK, itemlistbox, progress indicator etc

File upload, file download

Value selectorsSVS, EVS, OVS

Validations (Range, length, datatype)

Local dictionary, simple type, structures, java native typesComponent object model

Business graphics

Adobe Interactive formsMicrosoft office integration


22/23

Data binding, table binding, structure binding.

Context mapping, model binding, views, view sets

Various controllersError handling, message editor, messages

Webdynpro internationlization

Debugging techniques in webdynproModels, developing custom BAPIs/RFCs

Using calculated attributes, supply functions

Types of modelsAdaptive RFC model

Webservice model

Java bean model

Creating webdynpro application as IviewSLD config, JCO destinations

Popup, external, confirmation diaglog windows


Application and URL parametersWebdynpro service and Helper classes

Dynamic programmingFine tuning and performance issues

Reuse concepts of development components

Reading data and values from properties files.

VISUAL COMPOSER

Visual composer setupVC architecture

Forms, tables, image manager

Value helpsFormulas

Visual composer internationalization

Data intensive operationsSearching, sorting, filtering, aggregates

Entry lists:

Static, dynamic

Data services:BAPIs/RFCs

Webservices

BI queries

Web Dynpro for ABAP | webdynpro samplesand tutorial


23/23

WebDynpro for ABAP (WD4A, WDA) is the SAP standard UI ( user interface) technology for

developing Web applications in the ABAP language. It consists of a runtime environment and

a graphical development environment with special Web Dynpro tools that are integrated in

the ABAP Workbench (SE80).

Web Dynpro offers the following advantages for application developers:

The use of declarative and graphical tools significantly reduces the

implementation effort

Web Dynpro supports a structured design process

Strict separation between layout and business data

Reuse and better maintainability by using components

The layout and navigation is easily changed using the Web Dynpro tools

Stateful applications are supported that is, if the page is changed and the

required data remains intact so that you can access it at any time throughout the entire

application context.

Note that stateless applications are not possible.

Automatic data transport using data binding

Automatic input check

User interface accessibility is supported

Full integration in the reliable ABAP development environment

prob questions

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