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[SPAM] [obm-l] Probabilidade da união
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- Subject: [SPAM] [obm-l] Probabilidade da união
- From: "carry_bit" <carry_bit@xxxxxxxxxxxx>
- Date: Sat, 19 May 2007 20:57:57 -0300
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Ol=E1 integrantes da OBM-L,=20
=20
em probabilidade temos os seguintes
=20
Teorema 1: Se A e B s=E3o dois eventos quaisquer, ent=E3o=20
=20
P(A U B) =3D P(A) + P(B) =96 P(A inter B).
=20
=20
Teorema 2: Se A, B e C s=E3o tr=EAs eventos quaisquer, =
ent=E3o
=20
P(A U B U C) =3D P(A) + P(B) + P(C) =96 P(A =
inter B) =96
P(A inter C) =96 P(B inter C) + P(A inter B inter C).
=20
=20
Eu estou com dificuldade em demonstrar o Teorema 2. Estou partindo do =
lado
esquerdo da igualdade, tomando=20
=20
(A U B U C) =3D [(A U B) U C]
=20
e aplicando o Teorema 1. Entretanto n=E3o consigo encontrar o termo P(A =
inter
B inter C) do lado esquerdo da igualdade.
=20
Aguardo sugest=F5es para a demonstra=E7=E3o.
=20
Obrigado, carry_bit.
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<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Ol=E1 integrantes da <b><span
style=3D'font-weight:bold'>OBM-L</span></b>, =
<o:p></o:p></span></font></p>
<p class=3DMsoNormal style=3D'margin-left:35.4pt'><font size=3D2 =
color=3Dgreen
face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial;color:green'><o:p> </o:p=
></span></font></p>
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>em probabilidade temos os =
seguintes<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal style=3D'text-indent:35.4pt'><b><u><font size=3D2 =
face=3DArial><span
style=3D'font-size:10.0pt;font-family:Arial;font-weight:bold'>Teorema =
1:</span></font></u></b><u><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'> </span></font></u><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'>Se A e B s=E3o
dois eventos quaisquer, ent=E3o <o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'> =
&=
nbsp;
P(A U B) =3D P(A) + P(B) – P(A </span></font><font =
size=3D1
face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial'>inter</span></font><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'> =
B).<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'> =
<b><u><span style=3D'font-weight:bold'>Teorema 2:</span></u></b> Se A, B =
e C s=E3o
tr=EAs eventos quaisquer, ent=E3o<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'> =
&=
nbsp;
P(A U B U C) =3D P(A) + P(B) + P(C) – P(A =
</span></font><font
size=3D1 face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial'>inter</span></font><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'> B) –
P(A </span></font><font size=3D1 face=3DArial><span =
style=3D'font-size:8.0pt;
font-family:Arial'>inter</span></font><font size=3D2 face=3DArial><span
style=3D'font-size:10.0pt;font-family:Arial'> C) – P(B =
</span></font><font
size=3D1 face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial'>inter</span></font><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'> C) + P(A =
</span></font><font
size=3D1 face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial'>inter</span></font><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'> B </span></font><font
size=3D1 face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial'>inter</span></font><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'> =
C).<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'> =
<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Eu estou com dificuldade em =
demonstrar o
T<u>eorema 2.</u> Estou partindo do lado esquerdo da igualdade, tomando =
<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p> </o:p></span></font></p>=
<p class=3DMsoNormal style=3D'text-indent:35.4pt'><font size=3D2 =
color=3Dgreen
face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial;color:green'>(A U B
U C) =3D [(A U B) U C]<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p> </o:p></span></font></p>=
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>e aplicando o T<u>eorema 1</u>.
Entretanto n=E3o consigo encontrar o termo P(A </span></font><font =
size=3D1
color=3Dgreen face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial;
color:green'>inter</span></font><font size=3D2 color=3Dgreen =
face=3DArial><span
style=3D'font-size:10.0pt;font-family:Arial;color:green'> B =
</span></font><font
size=3D1 color=3Dgreen face=3DArial><span =
style=3D'font-size:8.0pt;font-family:Arial;
color:green'>inter</span></font><font size=3D2 color=3Dgreen =
face=3DArial><span
style=3D'font-size:10.0pt;font-family:Arial;color:green'> C) do lado =
esquerdo da
igualdade.<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p> </o:p></span></font></p>=
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Aguardo sugest=F5es para a =
demonstra=E7=E3o.<o:p></o:p></span></font></p>
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p> </o:p></span></font></p>=
<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Obrigado, =
carry_bit.</span></font><font
size=3D2 face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial'><o:p></o:p></span></font></p=
>
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