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[SPAM] [obm-l] Probabilidades e o Primeiro Lema de Kaplansky

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Subject: [SPAM] [obm-l] Probabilidades e o Primeiro Lema de Kaplansky
From: "Ulysses Coelho de Souza Jr." <ucsjr@xxxxxxxxxx>
Date: Sat, 22 Mar 2008 20:58:56 -0300
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	charset="iso-8859-1"
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Ol=E1 a todos,



A quest=E3o abaixo =E9 de um vestibular recente. Acredito que o =
examinador quis dizer "pelo menos um par" ao inv=E9s de "um par".



Coment=E1rios ser=E3o bem-vindos.=20



No Concurso da Mega-Sena s=E3o sorteados

6 n=FAmeros de 01 a 60. Por exemplo, o concurso

924 teve como n=FAmeros sorteados

02,20,21,27,51 e 60, ou seja, houve um par de

n=FAmeros consecutivos, 20 e 21. A probabilidade

de que no jogo da Mega-Sena haja um par de

n=FAmeros consecutivos sorteados =E9:

=20

(A) 54!/60!

(B) 53!/59!

(C) 1-(56!55!)/(49!60!)

(D) 1-(54!53!)/(48!60!)

(E) 1-(55!54!)/(49!60!)

Um abra=E7o,

Ulysses C. de Souza.
------=_NextPart_000_0007_01C88C5F.8B44E8F0
Content-Type: text/html;
	charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.6000.16608" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff><FONT color=3D#000080>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000 size=3D2>Ol=E1 a todos,</FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000 size=3D2></FONT></SPAN>&nbsp;</P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000 size=3D2>A quest=E3o abaixo =E9 de um vestibular =
recente.&nbsp;Acredito=20
que o examinador quis dizer "pelo menos um par" ao inv=E9s de "um=20
par".</FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"></SPAN>&nbsp;</P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000 size=3D2>Coment=E1rios ser=E3o =
bem-vindos.</FONT>&nbsp;</SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000 size=3D2></FONT></SPAN>&nbsp;</P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>No Concurso da Mega-Sena s=E3o =
sorteados<?xml:namespace=20
prefix =3D o ns =3D "urn:schemas-microsoft-com:office:office"=20
/><o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>6 n=FAmeros de 01 a 60. Por exemplo, o=20
concurso<o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>924 teve como n=FAmeros=20
sorteados<o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>02,20,21,27,51 e 60, ou seja, houve um =
par=20
de<o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>n=FAmeros consecutivos, 20 e 21. A=20
probabilidade<o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>de que no jogo da Mega-Sena haja um par=20
de<o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><FONT=20
color=3D#000000><FONT size=3D2>n=FAmeros consecutivos sorteados=20
=E9:<o:p></o:p></FONT></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><SPAN=20
style=3D"FONT-SIZE: 11pt; FONT-FAMILY: 'Arial','sans-serif'; =
mso-fareast-language: EN-US"><o:p><FONT=20
color=3D#000000 size=3D2>&nbsp;</FONT></o:p></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><FONT color=3D#000000><SPAN><FONT size=3D2>(A)=20
54!/60!<o:p></o:p></FONT></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><FONT color=3D#000000><SPAN><FONT size=3D2>(B)=20
53!/59!<o:p></o:p></FONT></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><FONT color=3D#000000><SPAN><FONT size=3D2>(C)=20
1-(56!55!)/(49!60!)<o:p></o:p></FONT></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-pagination: =
widow-orphan; tab-stops: 35.4pt"=20
align=3Dleft><FONT color=3D#000000><SPAN><FONT size=3D2>(D)=20
1-(54!53!)/(48!60!)<o:p></o:p></FONT></SPAN></FONT></P>
<DIV><FONT color=3D#000000 size=3D2><SPAN>(E)<STRONG>=20
</STRONG>1-(55!54!)/(49!60!)</SPAN></FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2><SPAN></SPAN></FONT>&nbsp;</DIV>
<DIV><FONT color=3D#000000 size=3D2><SPAN>Um =
abra=E7o,</SPAN></FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2><SPAN></SPAN></FONT>&nbsp;</DIV>
<DIV><FONT color=3D#000000 size=3D2><SPAN>Ulysses C. de=20
Souza.</SPAN></FONT></FONT></DIV></BODY></HTML>

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