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![](3D"master09_image001.gif")
Probability
Chapter 12=
The Nature of Probability
![](3D"master08_image002.gif")
![](3D"master08_image003.gif")
![](3D"master08_image004.gif")
Probability
Definitions
pExperiment: A contro=
lled
operation that yields a set of results
pOutcomes: Possible
results of an experiment
pEvent: Sub-coll=
ection
of outcomes of an experiment
Types
of Probability
pTheoretical Probability (Mathematical): Determined through a stu=
dy of possible outcomes
pEmpirical Probability (Experimental): Relative frequency of occurrence =
of an
event determined by actual observations of an experiment
Example of Theoretical vs. Empirical Probability
pSuppose we flip a fair coin
pWhat is the percent chance of flipping a head?
p50%
pThis is Theoretical Probability
Example of Theoretical vs. =
=
Empirical
Probability (cont.)
<=
/div>
![](3D"slide0322_image005.gif")
pFlip
a coin 10 times and record the results
Flip 10<=
/b>
Flip 9
Flip 8
Flip 7
Flip 6
Flip 5
Flip 4
Flip 3
Flip 2
Flip 1
Example of Theoretical vs. =
=
Empirical
Probability (cont.)
<=
/div>
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n Living Room: purple, orange, or green
=
;
n Dining Room: green, red, or yellow
n Kitchen: blue or red
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n Two socks are blue
<=
/span>
n Two are tan
<=
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n Two are white
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else
{
sId =3D RemoveFilePrefixFromHref(location.href);
var regExp =3D /\//
var fixedHref =3D sId
var pos =3D -1
=09
pos =3D fixedHref.search(regExp)
while (pos !=3D -1)
{
fixedHref =3D fixedHref.replace(regExp, "\\")
pos =3D fixedHref.search(regExp)
}
=09
if (g_fBaseHyperlink =3D=3D true)
sId =3D "file:///" + fixedHref;
else
sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1)
}
=09
return sId
}
function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx=
tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl=
e.display=3D'none'; return true } return false }
function IsWin( name ) { return window.name =3D=3D name }
function IsNts() { return IsWin("PPTNts") }
function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) }
function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"=
&& navigator.appVersion.indexOf("Windows")>0 ) }
function SupportsPPTHTML()
{
var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0
if( msie >=3D 0 )
ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) )
else
ver=3DparseInt(appVer)
return( ver >=3D 4 && msie >=3D 0 )
}
function _RSW()
{
if( !g_supportsPPTHTML || IsNts() ||
( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) )
return
var padding=3D0;
if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6
cltWidth=3Ddocument.body.clientWidth-padding
cltHeight=3Ddocument.body.clientHeight-padding
factor=3D(1.0*cltWidth)/g_origW
if( cltHeight < g_origH*factor )
factor=3D(1.0*cltHeight)/g_origH
newSize =3D g_origSz * factor
if( newSize < 1 ) newSize=3D1
s=3DSlideObj.style
s.fontSize=3DnewSize+"px"
s.posWidth=3Dg_origW*factor
s.posHeight=3Dg_origH*factor
s.posLeft=3D(cltWidth-s.posWidth+padding)/2
s.posTop=3D(cltHeight-s.posHeight+padding)/2
if( g_scaleHyperlinks )
ScaleHyperlinks( factor )
}
function _InitAnimations()
{
animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined';
isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode();
g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc=
reen && parent.IsSldVisited());
if( g_animUseRuntime ) {
collSeq =3D document.all.tags("seq");
if( collSeq !=3D null ) {
for(ii=3D0;ii numSlds )
gSldJumpIdx =3D numSlds;
if ( gSldJumpIdx >=3D 0 ) {
if ( gSldJumpIdx =3D=3D 0 )
gSldJumpIdx =3D 1;
var jumpTo =3D parseInt(gSldJumpIdx);
gSldJump =3D 0; gSldJumpIdx =3D "";
win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref )
}
}
}
function _KDH()
{
if( event.keyCode =3D=3D 8 ) {
event.returnValue =3D 0;
parent.GoToPrevSld();
}
}function DocumentOnClick()
{
if( IsNts() || parent.HideMenu() ) return;
if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames=
Mode() ) ||
(event && event.keyCode=3D=3D32) ) {
=09
if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex=
t )
return;
parent.GoToNextSld();
}
}
var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""=
, g_bgSound=3D"",
g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser =
=3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1;
var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w=
indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va=
r g_animManager =3D null;
var g_animUseRuntime =3D false;
var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime;
var g_animMainSequence =3D null;
var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram=
es", gIsEndShow=3D0, NUM_VIS_SLDS=3D47, SCRIPT_HREF=3D"script.js", FULLSCR_=
HREF=3D"fullscreen.htm";
var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO=
tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true
window.gPPTHTML=3DSupportsPPTHTML()
var g_fBaseHyperlink =3D false;
var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(=
"slide0317.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("=
slide0011.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("s=
lide0322.htm",1,-1,1),new hrefList("slide0325.htm",1,-1,1),new hrefList("sl=
ide0031.htm",1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("sli=
de0326.htm",1,-1,1),new hrefList("slide0318.htm",1,-1,1),new hrefList("slid=
e0327.htm",1,-1,1),new hrefList("slide0328.htm",1,-1,1),new hrefList("slide=
0329.htm",1,-1,1),new hrefList("slide0049.htm",1,-1,1),new hrefList("slide0=
330.htm",1,-1,1),new hrefList("slide0331.htm",1,-1,1),new hrefList("slide00=
70.htm",1,-1,1),new hrefList("slide0319.htm",1,-1,1),new hrefList("slide008=
0.htm",1,-1,1),new hrefList("slide0320.htm",1,-1,1),new hrefList("slide0100=
.htm",1,-1,1),new hrefList("slide0118.htm",1,-1,1),new hrefList("slide0129.=
htm",1,-1,1),new hrefList("slide0321.htm",1,-1,1),new hrefList("slide0139.h=
tm",1,-1,1),new hrefList("slide0141.htm",1,-1,1),new hrefList("slide0149.ht=
m",1,-1,1),new hrefList("slide0158.htm",1,-1,1),new hrefList("slide0165.htm=
",1,-1,1),new hrefList("slide0170.htm",1,-1,1),new hrefList("slide0176.htm"=
,1,-1,1),new hrefList("slide0182.htm",1,-1,1),new hrefList("slide0192.htm",=
1,-1,1),new hrefList("slide0197.htm",1,-1,1),new hrefList("slide0305.htm",1=
,-1,1),new hrefList("slide0306.htm",1,-1,1),new hrefList("slide0307.htm",1,=
-1,1),new hrefList("slide0309.htm",1,-1,1),new hrefList("slide0311.htm",1,-=
1,1),new hrefList("slide0313.htm",1,-1,1),new hrefList("slide0332.htm",1,-1=
,1),new hrefList("slide0314.htm",1,-1,1),new hrefList("slide0315.htm",1,-1,=
1),new hrefList("slide0324.htm",1,-1,1),new hrefList("slide0316.htm",1,-1,1=
),new hrefList("slide0323.htm",1,-1,1));
/*********************************************
Frameset functions
These functions control slide navigation
and state of the frameset.
**********************************************/
function RemoveFilePrefixFromHref(href)
{
var regExp =3D /^file:\/\/\//i;
return href.replace(regExp, "")
}
function FullScrInit()
{
g_allowAdvOnClick =3D GetCurSld().mAdvOnClk
document.body.style.backgroundColor=3D"black"
document.oncontextmenu=3Dparent._CM;
document.onkeydown =3D _KDH;
document.ondragstart=3DCancel
document.onselectstart=3DCancel
self.focus()
}
function Redirect( frmId )
{=09
var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId()
if(idx>=3D0) str=3Dstr.substr(1);
if( window.name !=3D frmId && ( sId !=3D str) ) {
obj =3D GetObj("Main-File")
window.location.href=3Dobj.href+"#"+sId
return 1
}
return 0
}
var MHTMLPrefix =3D CalculateMHTMLPrefix();=20
function CalculateMHTMLPrefix()
{
if ( document.location.protocol =3D=3D 'mhtml:') {=20
href=3Dnew String(document.location.href)=20
Start=3Dhref.indexOf('!')+1=20
End=3Dhref.lastIndexOf('/')+1=20
if (End < Start)=20
return href.substring(0, Start)=20
else=20
return href.substring(0, End)=20
}
return '';
}
function GetTags(base,tag)
{
if(g_supportsPPTHTML) return base.all.tags(tag);
else return base.getElementsByTagName(tag);
}
function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP=
refix+GetHrefObj( gCurSld ).mNtsHref ) }
function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() }
function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() }
function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() }
function SetHasNts( fVal )
{
if( gHasNts !=3D fVal ) {
gHasNts=3DfVal
UpdNavPane()
}
}
function ToggleOtlText()
{
gOtlTxtExp=3D!gOtlTxtExp
UpdOtlPane()
}
function ClearMedia()
{
// Clear any sounds playing before launching another browser window. Other=
wise,
// in fullscreen mode, you'll continue to hear the sound in the frames mod=
e.
if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0;
}
function FullScreen()
{=20
if ( PPTSld.g_animUseRuntime )
PPTSld.document.body.pause();
ClearMedia();
var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF =
: FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref;
if (MHTMLPrefix !=3D "")
href =3D RemoveFilePrefixFromHref(href)
if(PPTNav.event.ctrlKey) {
var w =3D (window.screen.availWidth * 1.0) / 2.0
var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW
win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top=
=3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h );
if( win.document.body && PPTSld.g_animUseRuntime )
win.document.body.PPTSldFrameset=3Dwindow;
}
else
{
win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" );
if( win.document.body && PPTSld.g_animUseRuntime )
win.document.body.PPTSldFrameset=3Dwindow;
}
}
function ToggleVNarration()
{
rObj=3DPPTSld.document.all("NSPlay")
if( rObj && !PPTSld.g_animUseRuntime ) {
if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) )
rObj.Play()
else if( rObj.playState =3D=3D 2 )
rObj.Pause()
else
return;
}
else if( PPTSld.g_animUseRuntime )
{
narObj =3D PPTSld.document.all("narrationID")
if( narObj )
narObj.togglePause()
}
}
function GetCurSldNum()
{ =20
obj=3DGetHrefObj(gCurSld)
if( obj.mOrigVis =3D=3D 1 )
return obj.mSldIdx
else =20
return gCurSld
}
function GetNumSlds()
{ =20
if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 )
return GetSldList().mNumVisSlds;
else
return GetSldList().mList.length
}
function GetSldNum( href )
{
for(ii=3D0; ii 1 )
PopSldList();
else if( !IsFramesMode() ) {
if( gLoopCont )
GoToFirst()
else
EndShow()
}
}
function GoToPrevSld()
{
ii=3DgCurSld-1
if( ii > 0 ) {
obj=3DGetHrefObj(ii)
while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) )
obj=3DGetHrefObj(--ii)
if( ii =3D=3D 0 ) ii=3D1
GoToSldNum(ii)
}
}
function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }
function GoToLast()
{
ii=3DGetSldList().mList.length
if( ii !=3D gCurSld )
GoToSld( GetHrefObj(ii).mSldHref )
}
function GoToSldNum( num )
{
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
obj =3D GetHrefObj( num )
obj.mVis=3D1
gPrevSld=3DgCurSld
gCurSld =3D num;
=09
if (MHTMLPrefix !=3D "")
PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref=
))
else
PPTSld.location.replace(obj.mSldHref)
=09
if( IsFramesMode() ) {
UpdNavPane(); UpdOtlPane(); UpdNtsPane()
}
}
function GoToSld( href )
{
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
GetHrefObj( GetSldNum(href) ).mVis=3D1
if (MHTMLPrefix !=3D "")
PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href))
else
PPTSld.location.replace(href)
}
function SldUpdated( id )
{
if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return
gPrevSld=3DgCurSld
gCurSld=3DGetSldNum(id)
if( IsFramesMode() ) {
UpdNavPane(); UpdOtlPane(); UpdNtsPane()
}
}
function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }
function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO=
bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) }
function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) }
function CloseWindow() {
if( HideMenu() ) return;
=09
var event =3D PPTSld.event;
if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D=
=3D32 || event.type=3D=3D"click" ) )
window.close( self );
CatchNumKeys( self, event );
}
function Unload() { gIsEndShow=3D0; }
function SetupEndShow() {
gIsEndShow=3D1;
PPTSld.document.body.scroll=3D"no";
PPTSld.document.onkeypress=3DCloseWindow;
PPTSld.document.onclick=3DCloseWindow;
PPTSld.document.oncontextmenu=3D_CM;
}
function EndShow()
{
if( IsFramesMode() ) return
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
doc=3DPPTSld.document
var dir =3D doc.body.dir
if( dir !=3D "rtl" ) dir =3D "ltr";
doc.open()
doc.writeln(' 0) {
PushSldList(sldList,fEnd);
gCurSld =3D 1;
}
else
if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
}
function PushSldList(arr,fEnd) {
var ii =3D gSldStack.length;
gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);
GoToSld( gSldStack[ii].mList[0].mSldHref );
}
function PopSldList() {
if (gSldStack[gSldStack.length-1].fEndShow)
EndShow()
else {
gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;
gSldStack[gSldStack.length-1] =3D null;
gSldStack.length--;
var sldList =3D gSldStack[gSldStack.length-1];
GoToSld( sldList.mList[gCurSld - 1].mSldHref );
}
}
var custShowList=3Dnew Array();
/*********************************************
Navigation button implementation
There are 2 types of buttons: ImgBtn, TxtBtn
implemented as function objects. They share
a similiar interface so the event handlers
can call SetActive, for example, on a button=20
object without needing to know exactly=20
what type of button it is.
**********************************************/
//----------------------------------
function ImgBtn( oId,bId,w,action )
//----------------------------------
{
var t=3Dthis
t.Perform =3D _IBP
t.SetActive =3D _IBSetA
t.SetInactive=3D _IBSetI
t.SetPressed =3D _IBSetP
t.SetDisabled=3D _IBSetD
t.Enabled =3D _IBSetE
t.ChangeIcon =3D null
t.UserAction =3D action
t.ChgState =3D _IBUI
t.mObjId =3D oId
t.mBorderId=3D bId
t.mWidth =3D w
t.mIsOn =3D t.mCurState =3D 0
}
function _IBSetA()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _IBSetI()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0=20
}
}
function _IBSetP()
{
if( this.mIsOn ) {
obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )
obj.style.posLeft+=3D1; obj.style.posTop+=3D1
}
}
function _IBSetD()
{ =20
obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )
obj.style.posTop=3D0=20
}
function _IBSetE( state )
{
var t=3Dthis
GetObj( t.mBorderId ).style.visibility=3D"visible"
if( state !=3D t.mIsOn ) {
t.mIsOn=3Dstate
if( state )
t.SetInactive()
else
t.SetDisabled()
}
}
function _IBP()
{
var t=3Dthis
if( t.mIsOn ) {
if( t.UserAction !=3D null )
t.UserAction()
if( t.ChangeIcon ) {
obj=3DGetObj(t.mObjId)
if( t.ChangeIcon() )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth
else
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth
}
t.SetActive()
} =20
}
function _IBUI( clr1,clr2,nextState )
{
var t=3Dthis
SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
obj=3DGetObj( t.mObjId )
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj=
.style.posTop
t.mCurState=3DnextState
return obj
}
//-----------------------------------------
function TxtBtn( oId,oeId,action,chkState )
//-----------------------------------------
{
var t=3Dthis
t.Perform =3D _TBP
t.SetActive =3D _TBSetA
t.SetInactive=3D _TBSetI
t.SetPressed =3D _TBSetP
t.SetDisabled=3D _TBSetD
t.SetEnabled =3D _TBSetE
t.GetState =3D chkState
t.UserAction =3D action
t.ChgState =3D _TBUI
t.mObjId =3D oId
t.m_elementsId=3D oeId
t.mIsOn =3D 1
}
function _TBSetA()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gHiliteClr,gShadowClr,0,0 )
}
function _TBSetI()
{
var t=3Dthis
if( t.mIsOn && !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
}
function _TBSetP()
{
if( this.mIsOn )
this.ChgState( gShadowClr,gHiliteClr,1,1 )
}
function _TBSetD()
{ =20
this.ChgState( gFaceClr,gFaceClr,0,0 )
this.mIsOn =3D 0
}
function _TBSetE()
{
var t=3Dthis
if( !t.GetState() )
t.ChgState( gFaceClr,gFaceClr,0,0 )
else
t.ChgState( gShadowClr,gHiliteClr,1,1 )
t.mIsOn =3D 1
}
function _TBP()
{
var t=3Dthis
if( t.mIsOn ) {=20
if( t.UserAction !=3D null )
t.UserAction()
if( !t.GetState )
return
if( t.GetState() )
t.SetPressed()
else
t.SetActive()
} =20
}
function _TBUI( clr1,clr2,lOffset,tOffset )
{
SetBorder( GetObj( this.mObjId ),clr1,clr2 )
Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
}
function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle=
ft }
function SetBorder( obj, upperLeft, lowerRight )
{
s=3Dobj.style;
s.borderStyle =3D "solid"
s.borderWidth =3D 1=20
s.borderLeftColor =3D s.borderTopColor =3D upperLeft
s.borderBottomColor=3D s.borderRightColor =3D lowerRight
}
function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }
function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }
function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() }
function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() }
function BtnOnUp()
{
b=3DGetBtnObj()
if( b !=3D null )
b.Perform()
else
Upd()
}
function GetNtsState(){ return parent.gNtsOpen }
function GetOtlState(){ return parent.gOtlOpen }
function GetOtlTxtState(){ return parent.gOtlTxtExp }
function NtsBtnSetFlag( fVal )
{
s=3Ddocument.all.item( this.m_flagId ).style
s.display=3D"none"
if( fVal )
s.display=3D""
else
s.display=3D"none"
}
function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etActive() }
function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etInactive() }
function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etPressed() }
function _BSetA_BorderImg()
{=20
b =3D gBtnArr[this.mBorderId]=20
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
obj.style.posTop=3D0
}
}
function _BSetI_BorderImg()
{=20
b =3D gBtnArr[this.mBorderId]
if( b !=3D null && this.mIsOn && !b.GetState() ) {
obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
obj.style.posTop=3D0
}
}
var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=
THREEDFACE"
var gBtnArr =3D new Array()
gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=
e,GetOtlState )
gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=
lPane,GetOtlState )
gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN=
tsPane )
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Creating the DIVs using createElement() means
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------=_NextPart_01CA8E18.46564A60
Content-Location: file:///C:/6E4BB24E/chapter_12_presentation_files/fullscreen.htm
Content-Transfer-Encoding: quoted-printable
Content-Type: text/html; charset="us-ascii"
Chapter 12: Probability
------=_NextPart_01CA8E18.46564A60--
pWhat percent heads did you flip?
pThis is Empirical Probability
<=
span
class=3DBB style=3D'position:absolute;left:-4.18%;top:.3em'>pWill the Theoretical and
Empirical probabilities always match?
pNo!
Law
of Large Numbers
pProbability statements apply in practice to a large number of trials
pProbability statements do not apply to a single trial&#=
13;
pIndividual events or precise totals are not predictable=
Determining Empirical Probability
pProbability of an Event:
P(E) =3D number = of times event E has occurred
total = times experiment has been performed
P(E) =3D number = of times event E has occurred
total = times experiment has been performed
<=
span
style=3D'font-size:86%;visibility:hidden'>p&#=
13;
Example
pForty people were surveyed on their
favorite flavor of ice cream
pThe results follow
pFind the empirical probability that a
person liked each flavor of ice cream
Example: Ice =
Cream
Survey
7
Other
4
Strawberry
11
Chocolate
18
Vanilla
Empirical Probability
Computation
Survey
Results
Flavor
Example: Ice =
Cream
Survey
7/40
7
Other
4/40
4
Strawberry
11/40
11
Chocolate
18/40
18
Vanilla
Empirical Probability
Computation
Survey
Results
Flavor
Example: Ice =
Cream
Survey
17.5%
7/40
7
Other
10%
4/40
4
Strawberry
27.5%
11/40
11
Chocolate
45%
18/40
18
Vanilla
Empirical Probability
Computation
Survey
Results
Flavor
Example
p55 people were surveyed on the numb=
er
of siblings (brothers and/or sisters) in their family
=
pThe results follow
<=
span
class=3DBB style=3D'position:absolute;left:-3.91%;top:.3em'>pFind t=
he
empirical probability that a person had the following number of sibl=
ings
Example: Sibling Survey
3
Other
4
4
10
3
17
2
13
1
8
0
Empirical Probability
Computation
Survey
Results
#
of Siblings
Example: Sibling Survey
3/55
3
Other
4/55
4
4
10/55
10
3
17/55
17
2
13/55
13
1
8/55
8
0
Empirical Probability
Computation
Survey
Results
#
of Siblings
Example: Sibling Survey
5.45%
3/55
3
Other
7.27%
4/55
4
4
18.18%
10/55
10
3
30.91%
17/55
17
2
23.64%
13/55
13
1
14.55%
8/55
8
0
Empirical Probability
Computation
Survey
Results
#
of Siblings
Theoretical
Probability
Theoretical Probability
pEqually Likely Outcomes: Experiment in which all outcomes have the same c=
hance
of occurring
pProbability in an Experiment with Equally Likely Outcomes:
P(E) =3D number of outcomes favorable to E
total number of possible ou= tcomes
P(E) =3D number of outcomes favorable to E
total number of possible ou= tcomes
Example
pA
card is drawn from a standard deck of cards. Find the probability of
drawing:
<=
span
style=3D'mso-hansi-font-family:"Times New Roman";display:none'>
pan ace
=
;
n4/ 52 =3D
1/13
pa face car=
d
n12/ 52 =3D
4/13
pan eleven&=
#13;
n0/ 52 =3D
0
Example (cont.)
pa heart=
3;
n13/52 =3D
1/4
panything b=
ut a
heart
n39/52 =3D
3/4
pa card sha=
ped
like a rectangle
n52/52 =3D
1
pa 4 or a
spade
n16/52 =3D
4/13
pa 4 and a
spade
n1/52
Properties
of Probability
1)The probability of an impossible event is 0
=
2)The probability of a certain event is 1
3)For any event, 0 ≤ P(E) ≤ 1
4)The sum of all
non-intersecting probabilities of an experiment is 1
5)An event must either occur or not occur
Therefore, P(E) + P(not E) =3D 1
Therefore, P(E) + P(not E) =3D 1
Example: =
A fair coin is flipped <=
/span>two times<=
/div>
a)Determine all possible outcomes
b)Find the probability of flipping two heads in a row
=
;
c)Find the probability of not
flipping two heads in a row
Example
pIn
the daily number, three ping pong balls are selected from three diff=
erent
machines. Each machine contains balls
numbered 0-9. Find the probability of:
a)hitting your favorite number
b)not hitting your favorite number
Odds
Section 12.3
Odds
pCompares the probability of an event occurring to the <=
/span>probability of the event=
not
occurring
pUsed extensively in gambling situations (super bowl picks etc), as well as in
other life situations
Odds
Against (Most Common)
pA ratio of the probability that an event will fail to <=
/span>occur (failure) to the
probability that the event will occur (success)
<=
span
style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>pOdds Against =3D P(failure)
P(success)
P(success)
Example
pDetermine the odds against drawing an Ace from a deck of cards
pP(success) =3D 1/ 13
pP(failure) =3D 12/ 13
pOdds Against =3D
<=
span
style=3D'font-size:71%;visibility:hidden'>p
<=
span
style=3D'font-size:71%'>pNote: The denomina=
tors
will always cancel out since there are the same number of
possible outcomes for failure as for success
Example
pDetermine the odds against rolling a five or six on a <=
/span>die
pP(success) =3D 2/ 6
pP(failure) =3D 4/ 6
pOdds Against =3D
Odds
in Favor (Less Common)
pA ratio of the probability of success to the probabilit=
y of failure
pOdds in Favor =3D
=
P(success)
P(failure)
P(failure)
Example
pA fair coin is flipped two times. Find the odds in favor of flipping two he=
ads in
a row.
pP(success) =3D 1/ 4
pP(failure) =3D 3/ 4
pOdds in Favor =3D
Example
pTwo dice are rolled.&n=
bsp;
Find the odds in favor of rolling “snake
eyes” (two ones).
pP(success) =3D 1/ 36
pP(failure) =3D 35/ 36
pOdds in Favor =3D
Determining Probabilities
Given Odds
Given Odds
1)Find denominator of probabilities by adding both number in the odds
<=
/span>
2)Use the first number from odds for the probability of failure (assuming odds
against)
3)Use the second number from odds for the <=
span
style=3D'position:absolute;top:51.02%;left:7.18%;width:92.81%;height:48.97=
%'>probability of success
(assuming odds against)
Note) The numbers are switched if it is odds in favor<=
/div>
Example
pThe
odds against winning the daily number are 999/1. Find the probability of winning a=
nd the
pro=
bability
of losing.
1)999 + 1 =3D 1000
2)P(F) =3D 999<=
span
style=3D'mso-hansi-font-family:"Times New Roman"'>/1000
3)P(S) =3D 1/ 1000
Example
pThe
odds against the Pirates winning the World Series are 25,000/1. Find the probability of the Pirat=
es winning and the probabil=
ity of
the Pirates not winning.
1)25,000 + 1 =3D 25,001
2)P(F) =3D 25,000/25001
3)P(S) =3D 1/ 25001
Tree
Diagrams
Counting
Principle
pGiven two experiments with the first having M distinct outcomes and the
second having N distinct outcomes
<=
span
class=3DBB style=3D'position:absolute;left:-4.18%;top:.3em'>pThe experiments combined=
have
M ∙ N possible outcomes
Example
pWe roll two dice.
Find the number of possible outcomes.
pThe first die has 6 possible outcomes
pThe second die has 6 possible outcomes
<=
span
class=3DBB style=3D'position:absolute;left:-4.21%;top:.3em'>pThe two dice have 6 W=
29; 6
=3D 36 possible outcomes
Example
pWe flip three coins.&n=
bsp;
Find the number of possible outcomes.
pEach coin has two possible outcomes
<=
/div>
pAll three coins have 2 ∙ 2 ∙ 2 =3D 8 possib=
le
outcomes
Definitions
pSample
Space:<=
span
style=3D'mso-spacerun:yes'> List of all possible outcomes of =
an experiment
pTree Diagram: Graphica=
lly
displays the sample space for an experiment by using a “branch”=
for
each outcome
of each portion of the experiment
Example
pProduce the sample space for flipping three coins using
a tree diagram
Example
pA bag contains four chips colored blue, gree=
n,
red, and yellow. O=
ne
chip is selected and then, without replacement, a second ch=
ip
is selected. Produce the sample
space for this experiment using a tree diagram.
Example
pTwo
spins are given on a spinner that has 4 evenly-distributed colors on it=
, red,
blue, yellow, and green
A.How
many total outcomes? Us=
e the
counting principle
and a tree diagram.
B.What
is the probability of RedRed?
C.What
is the probability of at least one of the spins being Red?=
Example
<=
span
class=3DBB style=3D'position:absolute;left:-3.86%;top:.3em'>pBetty is going to paint =
her
living room, dining room and kitchen.
She’s narrowed the colors as follows:
pEach color is equally likely to be picked.
Example
(cont.)
A.How
many total outcomes? Us=
e the
counting principle
and a tree diagram.
B.What
is the probability of a color scheme that includes green?
C.What
is the probability of a color scheme that doesn’t include re=
d?
Example
pJill has six socks in a drawer
<=
span
class=3DBB style=3D'position:absolute;left:-4.35%;top:.3em'>pIn the dark, she selects=
one
sock, then without replacement, selects a second sock
Example
(cont.)
A.How
many total outcomes? Us=
e the
counting principle
and a tree diagram.
B.What
is the probability of selecting two tan socks?
C.What
is the probability selecting any “match”?
D.What
is the probability of not selecting a “match”?
' + ENDSHOW_MESG + '
![](3D"notes_flag.gif")
No=
tes![](3D"buttons.gif")
