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Cell[CellGroupData[{
Cell["Exercices compl\[EAcute]mentaires - 2 - Probabilit\[EAcute]s", \
"Subsection"],

Cell[CellGroupData[{

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        total, "\< personnes d\[CloseCurlyQuote]un \[AHat]ge donn\[EAcute], \
il y a \>", a, "\< cas de cancer du poumon. Sur ces \>", 
        total, "\< personnes, il y avait \>", c1, "\< fumeurs dont \>", 
        a1, "\< avaient le cancer du poumon.
Quelle est la probabilit\[EAcute] qu\[CloseCurlyQuote]une personne tir\
\[EAcute]e au hasard 
\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<a) n\[CloseCurlyQuote]ait pas le cancer du poumon;\>"];\)\), \
"\[IndentingNewLine]", 
    \(\(Print["\<b) soit un fumeur canc\[EAcute]reux;\>"];\)\), "\
\[IndentingNewLine]", 
    \(\(Print["\<c) soit un fumeur si on sait qu\[CloseCurlyQuote]elle est \
canc\[EAcute]reuse?\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<La cigarette influence-t-elle le fait d'avoir le cancer du \
poumon?\>"];\)\)}], "Input",
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\[InvisibleSpace]10000\[InvisibleSpace]" personnes, il y avait "\
\[InvisibleSpace]6000\[InvisibleSpace]" fumeurs dont "\[InvisibleSpace]300\
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\[EAcute] qu\[CloseCurlyQuote]une personne tir\[EAcute]e au hasard  "\),
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    \(TraditionalForm\`"b) soit un fumeur canc\[EAcute]reux;"\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"c) soit un fumeur si on sait qu\[CloseCurlyQuote]elle \
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Cell[BoxData[
    \(TraditionalForm\`"La cigarette influence-t-elle le fait d'avoir le \
cancer du poumon?"\)], "Print"],

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Cell["Solution:", "Subsubsection"],

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Cell[BoxData[{
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rentrer chez lui,il constate qu'il a perdu une clef.Il doit ouvrir sa porte \
qui comporte deux serrures.Trouver\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<a) la probabilit\[EAcute] qu'il sache ouvrir la \
porte;\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<b) la probabilit\[EAcute] qu'il puisse ouvrir la porte avec \
les deux premi\[EGrave]res clefs qu'il essaie.\>"];\)\), \
"\[IndentingNewLine]", 
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Cell[BoxData[
    \(TraditionalForm\`"2. Un homme a dans sa poche un trousseau de 6 \
clefs.Avant de rentrer chez lui,il constate qu'il a perdu une clef.Il doit \
ouvrir sa porte qui comporte deux serrures.Trouver"\)], "Print"],

Cell[BoxData[
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porte;"\)], "Print"],

Cell[BoxData[
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porte avec les deux premi\[EGrave]res clefs qu'il essaie."\)], "Print"],

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Cell["Solution:", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[{
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Cell[CellGroupData[{

Cell[BoxData[{
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        a, "\< \[EAcute]tudiants ont Abel comme professeur, \>", 
        b, "\< ont Baudouin comme professeur. \>", 
        a1, "\<  \[EAcute]tudiants d\[CloseCurlyQuote]Abel ont rat\[EAcute], \
\>", b1, "\< \[EAcute]l\[EGrave]ves de Baudouin ont rat\[EAcute].\>"];\)\), "\
\[IndentingNewLine]", 
    \(\(Print["\<a) un \[EAcute]l\[EGrave]ve ayant rat\[EAcute] est tir\
\[EAcute] au hasard. Quelle est la probabilit\[EAcute] qu\[CloseCurlyQuote]il \
ait Abel comme professeur?\>"];\)\), "\[IndentingNewLine]", 
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\[EAcute]l\[EGrave]ve quelconque ait rat\[EAcute] et soit un \[EAcute]l\
\[EGrave]ve de Baudouin?\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<c) Quelle est la probabilit\[EAcute] qu\[CloseCurlyQuote]un \
\[EAcute]l\[EGrave]ve choisi au hasard soit en \[EAcute]chec?\>"];\)\), "\
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\[InvisibleSpace]" \[EAcute]tudiants ont Abel comme professeur, "\
\[InvisibleSpace]60\[InvisibleSpace]" ont Baudouin comme professeur. "\
\[InvisibleSpace]10\[InvisibleSpace]"  \[EAcute]tudiants \
d\[CloseCurlyQuote]Abel ont rat\[EAcute], "\[InvisibleSpace]12\
\[InvisibleSpace]" \[EAcute]l\[EGrave]ves de Baudouin ont rat\[EAcute]."\),
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell["Solution:", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[{
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Cell[CellGroupData[{

Cell[BoxData[{
    \(\(n = 52;\)\), "\[IndentingNewLine]", 
    \(\(Print["\<4. Un test rapide pour d\[EAcute]tecter le cancer a \
\[EAcute]t\[EAcute] mis au point. Si un individu est canc\[EAcute]reux, il y \
a 95 chances sur 100 que le test r\[EAcute]agisse positivement. Par contre, \
s'il est sain, il y a quand m\[EHat]me 10 chances sur 100 que le test r\
\[EAcute]agisse positivement. Dans une population donn\[EAcute]e, on compte \
18,5 % de r\[EAcute]actions positives.\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<a) Si un individu est pris au hasard dans cette population, \
trouver la probabilit\[EAcute] qu'il soit canc\[EAcute]reux et \
r\[EAcute]agisse au test.\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<b) Trouver la proportion th\[EAcute]orique de \
canc\[EAcute]reux dans cette population.\>"];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<c) Si un individu choisi au hasard dans cette population a r\
\[EAcute]agi positivement au test, trouver la probabilit\[EAcute] que cet \
individu soit effectivement atteint du cancer.\>"];\)\)}], "Input",
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Cell[BoxData[
    \(TraditionalForm\`"4. Un test rapide pour d\[EAcute]tecter le cancer a \
\[EAcute]t\[EAcute] mis au point. Si un individu est canc\[EAcute]reux, il y \
a 95 chances sur 100 que le test r\[EAcute]agisse positivement. Par contre, \
s'il est sain, il y a quand m\[EHat]me 10 chances sur 100 que le test r\
\[EAcute]agisse positivement. Dans une population donn\[EAcute]e, on compte \
18,5 % de r\[EAcute]actions positives."\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"a) Si un individu est pris au hasard dans cette \
population, trouver la probabilit\[EAcute] qu'il soit canc\[EAcute]reux et r\
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Cell[BoxData[
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\[EAcute]reux dans cette population."\)], "Print"],

Cell[BoxData[
    \(TraditionalForm\`"c) Si un individu choisi au hasard dans cette \
population a r\[EAcute]agi positivement au test, trouver la probabilit\
\[EAcute] que cet individu soit effectivement atteint du cancer."\)], "Print"],

Cell[CellGroupData[{

Cell["Solution:", "Subsubsection"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(Print["\<b) P(cancer) = \>", 8.5/85];\)\), "\[IndentingNewLine]", 
    \(\(Print["\<a) P(test positif \[Intersection] cancer) = \>", 
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Cell[BoxData[{
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    \(\(Print["\<5. Un ranch poss\[EGrave]de \>", total, "\< chevaux (\>", 
        b, "\< blancs, \>", n, "\< noirs et \>", 
        g, "\< gris) et une cal\[EGrave]che pr\[EAcute]vue pour \[EHat]tre \
tir\[EAcute]e par 2 chevaux. Le cocher de la cal\[EGrave]che choisit au \
hasard les 2 chevaux de l\[CloseCurlyQuote]attelage, parmi les \>", 
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    \(\(Print["\<a) Calculer la probabilit\[EAcute] des \
\[EAcute]v\[EAcute]nements suivants :\>"];\)\), "\[IndentingNewLine]", 
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\[RightGuillemet],\>"];\)\), "\[IndentingNewLine]", 
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\[RightGuillemet],\>"];\)\), "\[IndentingNewLine]", 
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l\[CloseCurlyQuote]attelage sont de couleurs diff\[EAcute]rentes, quelle est \
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    \(\(Print["\<c) Des enfants effectuent un stage de \>", 
        j, "\< jours dans le ranch. Le cocher organise alors, chaque jour, \
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\[CloseCurlyQuote]attelage.\>"];\)\), "\[IndentingNewLine]", 
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\[EAcute]v\[EAcute]nements suivants:\>"];\)\), "\[IndentingNewLine]", 
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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