\documentclass[12pt]{article}\usepackage[Mickael]{ammaths}\begin{document}\en

\module{Translations and probabilities}{01}{11}{1 period}

\prereq{Events and probabilities}

\object{\begin{itemize}
        \item See the importance of language in probabilities.
	\item Practise some simple probability computations
\end{itemize}}

\mater{\begin{itemize}
	\item Sentences in different languages.
	\item Task sheets.
\end{itemize}}

\modpart{Events defined in various languages}{15 mins}

Students work in groups of 4.

The definitions of 7 events are given in English, German, Spanish, Catalan, Danish, Italian and Romanian.
Each group has to associate the sentences defining the same events in different languages.

\modpart{Simple probabilities}{10 mins}

Each group has to gather information around in the class to be able to compute the probabilities of the seven events, and other events defined using these ones.

\modpart{Intersections and unions}{Remaining time}

The intersection and union symbols are introduced by the teacher.

Some events are defined by one sentence in one language. Each event must be translated into English and then into the mathematical language, using the intersection and union symbols.

\begin{description}
\item[$M\cap B$ :] The randomly picked pupil is a boy and has blue eyes
\item[$M\cup F$ :] Tilf{\ae}ldigt udvalgt elev er en pige eller en dreng
\item[$M\cap S$ :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge und hat kurze Haare
\item[$S\cap D$ :] Tilf{\ae}ldigt udvalgt elev har kort h\aa{}r og brune \o{}jne
\item[$D\cup S$ :] Elev-a ales la {\^i}nt{\^a}mplare de par scurt sau maro ochi
\item[$B\cup D$ :] El alumno elegido al azar tiene los ojos azules o marrones
\item[$L\cup M$ :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge oder hat lange Haare
\item[$F\cap B\cap L$ :] L'alumne escollit a l'atzar \'{e}s una nena, t\'{e} el cabell llarg i ulls blaus
\item[$B\cup D\cup G$ :] Los ojos del alumno elegido al azar son azules, marrones o verdes,
\item[$F\cap G$ :] L'allievo scelto a caso \`e una ragazza e ha gli occhi verdi
\end{description}

\pagebreak

\moddocdis{Translations and probabilities}{01}{11}{Task sheet}

\sectionblack{Task 1 -- Translations}

A pupil is picked randomly in your half-class. Seven events related to this random experiment are defined below in English. On a separate paper, the same events are written in German, Spanish, Catalan, Danish, Italian and Romanian. Find the translations of each event is the 6 other languages.

\begin{description}
\item [M :] The randomly picked pupil is a boy.
\item [F :] The randomly picked pupil is a girl.
\item [B :] The randomly picked pupil has blues eyes.
\item [D :] The randomly picked pupil has brown eyes.
\item [G :] The randomly picked pupil has green eyes.
\item [L :] The randomly picked pupil has long hair.
\item [S :] The randomly picked pupil has short hair.
\end{description}

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\rowcolor{lightgray} Notation & German & Spanish & Catalan & Danish & Italian & Romanian \\
\hline
M &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
F &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
B &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
D &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
G &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
L &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
S &&&&&& \rule{0pt}{15pt}\\[5pt] \hline
\end{tabular}
\end{center}


\sectionblack{Task 2 -- Simple probabilities}

Find information in the class to compute the probabilities below. In the next part, more complicated events will be considered, so try to gather as much information as you can.


\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\cellcolor{lightgray} Event &\;\; M \;\; &\;\; F \;\; &\;\; B \;\; &\;\; D \;\; &\;\; G \;\; &\;\; L \;\; &\;\; S \;\; \\
\hline
\cellcolor{lightgray} Probability & & & & & & & \rule{0pt}{23pt}\\[12pt]
\hline
\end{tabular}
\end{center}


\pagebreak

\sectionblack{Task 3 -- Intersections and unions of events}

Below are defined, in other languages, 10 more events, intersections or unions of the seven first events. Translate each one in English and then in mathematics, using the notations for the initial events and the symbols $\cap$ and $\cup$. When it's done, find out the probability of each new event.






\begin{center}
\begin{tabular}{|c|p{4cm}|c|p{4cm}|}
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{The randomly picked pupil is a boy and has blue eyes.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Tilf{\ae}ldigt udvalgt elev er en pige eller en dreng.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge und hat kurze Haare.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Tilf{\ae}ldigt udvalgt elev har kort h\aa{}r og brune \o{}jne.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Elev-a ales la {\^i}nt{\^a}mplare de par scurt sau maro ochi.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\end{tabular}
\end{center}


\begin{center}
\begin{tabular}{|c|p{4cm}|c|p{4cm}|}
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{El alumno elegido al azar tiene los ojos azules o marrones.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge oder hat lange Haare.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{L'alumne escollit a l'atzar \'{e}s una nena, t\'{e} el cabell llarg i ulls blaus.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Los ojos del alumno elegido al azar son azules, marrones o verdes.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{L'allievo scelto a caso \`e una ragazza e ha gli occhi verdi.}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{}\rule{0pt}{15pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation & &\cellcolor{lightgray} Probability & \rule{0pt}{23pt}\\[12pt]
\hline
\end{tabular}
\end{center}








\pagebreak

\moddocdis{Translations and probabilities}{01}{11}{Translations}

\setcounter{page}{4}

\sectionblack{German}

\begin{description}
\item[G1 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler hat braune Augen
\item[G2 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler hat kurze Haare
\item[G3 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge
\item[G4 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler hat Blues Augen
\item[G5 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein M\"{a}dchen
\item[G6 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler hat lange Haare
\item[G7 :] Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler hat gr\"{u}ne Augen
\end{description}

\sectionblack{Spanish}

\begin{description}
\item[S1 :] El alumno elegido al azar tiene ojos marrones
\item[S2 :] El alumno elegido al azar tiene el pelo largo
\item[S3 :] El alumno elegido al azar es una ni\~{n}a
\item[S4 :] El alumno elegido al azar tiene los ojos azules
\item[S5 :] El alumno elegido al azar tiene el pelo corto
\item[S6 :] El alumno elegido al azar es un ni\~{n}o
\item[S7 :] El alumno elegido al azar tiene los ojos verdes
\end{description}

\sectionblack{Catalan}

\begin{description}
\item[C1 :] L'alumne escollit a l'atzar t\'{e} ulls marrons
\item[C2 :] L'alumne escollit a l'atzar \'{e}s un nen
\item[C3 :] L'alumne escollit a l'atzar t\'{e} els cabells llargs
\item[C4 :] L'alumne escollit a l'atzar t\'{e} els ulls blaus
\item[C5 :] L'alumne escollit a l'atzar t\'{e} els ulls verds
\item[C6 :] L'alumne escollit a l'atzar t\'{e} els cabells curts
\item[C7 :] L'alumne escollit a l'atzar \'{e}s una nena
\end{description}

\pagebreak

\sectionblack{Danish}

\begin{description}
\item[D1 :] Tilf{\ae}ldigt udvalgt elev har gr\o{}nne \o{}jne
\item[D2 :] Tilf{\ae}ldigt udvalgt elev er en pige
\item[D3 :] Tilf{\ae}ldigt udvalgt elev har brune \o{}jne
\item[D4 :] Tilf{\ae}ældigt udvalgt elev har bl\aa{} \o{}jne
\item[D5 :] Tilf{\ae}ldigt udvalgt elev har kort h\aa{}r
\item[D6 :] Tilf{\ae}ldigt udvalgt elev er en dreng
\item[D7 :] Tilf{\ae}ldigt udvalgt elev har langt h\aa{}r
\end{description}

\sectionblack{Italian}

\begin{description}
\item[I1 :] L'allievo scelto a caso \`{e} una ragazza
\item[I2 :] L'allievo scelto a caso, ha gli occhi azzurri
\item[I3 :] L'allievo scelto a caso \`{e} un ragazzo
\item[I4 :] L'allievo scelto a caso, ha gli occhi marroni
\item[I5 :] L'allievo scelto a caso ha i capelli lunghi
\item[I6 :] L'allievo scelto a caso, ha gli occhi verdi
\item[I7 :] L'allievo scelto a caso ha i capelli corti
\end{description}

\sectionblack{Romanian}

\begin{description}
\item[R1 :] Elev-a ales la {\^i}nt{\^a}mplare p\v{a}rul lung
\item[R2 :] Elev la {\^i}nt{\^a}mplare ales are ochii de blues
\item[R3 :] Elev la {\^i}nt{\^a}mplare ales este un b\v{a}iat
\item[R4 :] Elev la {\^i}nt{\^a}mplare ales are ochii maro
\item[R5 :] Elev la {\^i}nt{\^a}mplare ales este o fata
\item[R6 :] Elev la {\^i}nt{\^a}mplare culese are ochii verzi
\item[R7 :] Elev-a ales la {\^i}nt{\^a}mplare de p\v{a}r scurt
\end{description}


%%%%%%%%%%%%%%%%%%Corrections%%%%%%%%%%%%%%%%%
\pagebreak
\moddocdis{Translations and probabilities}{01}{11}{Correction}

\sectionblack{Task 1 -- Translations}

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\rowcolor{lightgray} Notation & German & Spanish & Catalan & Danish & Italian & Romanian \\
\hline
\cellcolor{lightgray}M &G3&S6&C2&D6&I3&R3 \rule{0pt}{15pt}\\[5pt] \hline
\cellcolor{lightgray}F &G5&S3&C7&D2&I1&R5 \rule{0pt}{15pt}\\[5pt] \hline
\cellcolor{lightgray}B &G4&S4&C4&D4&I2&R2 \rule{0pt}{15pt}\\[5pt] \hline
\cellcolor{lightgray}D &G1&S1&C1&D3&I4&R4 \rule{0pt}{15pt}\\[5pt] \hline
\cellcolor{lightgray}G &G7&S7&C5&D1&I6&R6 \rule{0pt}{15pt}\\[5pt] \hline
\cellcolor{lightgray}L &G6&S2&C3&D7&I5&R1 \rule{0pt}{15pt}\\[5pt] \hline
\cellcolor{lightgray}S &G2&S5&C6&D5&I7&R7 \rule{0pt}{15pt}\\[5pt] \hline
\end{tabular}
\end{center}


\sectionblack{Task 2 -- Simple probabilities}

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\cellcolor{lightgray} Event &\;\; M \;\; &\;\; F \;\; &\;\; B \;\; &\;\; D \;\; &\;\; G \;\; &\;\; L \;\; &\;\; S \;\; \\
\hline
\cellcolor{lightgray} Probability & & & & & & & \rule{0pt}{23pt}\\[12pt]
\hline
\end{tabular}
\end{center}



\pagebreak
\sectionblack{Task 3 -- Intersections and unions of events}
\begin{center}
\begin{tabular}{|c|p{4cm}|c|p{4cm}|}
\hline
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{The randomly picked pupil is a boy and has blue eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a boy and has blue eyes.}\rule{0pt}{12pt}
\\[5pt]
\hline
\cellcolor{lightgray} Notation &$M\cap B$&\cellcolor{lightgray} Probability & \rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Tilf{\ae}ldigt udvalgt elev er en pige eller en dreng.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a boy or a girl.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$M\cup F$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge und hat kurze Haare.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a boy and has short hair.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$M\cap S$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Tilf{\ae}ldigt udvalgt elev har kort h\aa{}r og brune \o{}jne.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil has short hair and brown
eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$S\cap D$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Elev-a ales la {\^i}nt{\^a}mplare de par scurt sau maro ochi.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil has short hair and brown eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$D\cap S$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{El alumno elegido al azar tiene los ojos azules o marrones.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil has blue eyes or brown eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$B\cup D$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Die zuf\"{a}llig ausgew\"{a}hlter Sch\"{u}ler ist ein Junge oder hat lange Haare.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a boy or has long hair.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$L\cup M$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{L'alumne escollit a l'atzar \'{e}s una nena, t\'{e} el cabell llarg i ulls blaus.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a girl with long hair and blues eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$F\cap B\cap L$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{Los ojos del alumno elegido al azar son azules, marrones o verdes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a boy or has brown or green eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$B\cup D\cup G$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\rowcolor{lightgray} Definition & \multicolumn{3}{|l|}{L'allievo scelto a caso \`e una ragazza e ha gli occhi verdi.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} English & \multicolumn{3}{|l|}{The randomly picked pupil is a girl and has green eyes.}\rule{0pt}{12pt}\\[5pt]
\hline
\cellcolor{lightgray} Notation &$F\cap G$ &\cellcolor{lightgray} Probability &\rule{0pt}{12pt}\\[5pt]
\hline%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{tabular}
\end{center}


\end{document}
