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%% This is file `prob-probspaces2.tex',
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%% The original source files were:
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%% probsoln.dtx  (with options: `prob-probspaces2.tex,package')
%% 
%%  probsoln.dtx
%%  Copyright 2013 Nicola Talbot
%% 
%%  This work may be distributed and/or modified under the
%%  conditions of the LaTeX Project Public License, either version 1.3
%%  of this license of (at your option) any later version.
%%  The latest version of this license is in
%%    http://www.latex-project.org/lppl.txt
%%  and version 1.3 or later is part of all distributions of LaTeX
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%%  This work has the LPPL maintenance status `maintained'.
%% 
%%  The Current Maintainer of this work is Nicola Talbot.
%% 
%%  This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex.
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%% randomly select 25 problems from derivatives.tex and add to
%% the data set called 'deriv'
%% Display the problems
%% You may need to change \theenumi back here
%% randomly select 25 problems from probspaces.tex and add to
%% the data set called 'spaces'
%% Display the problems
%% You may need to change \theenumi back here
 % This file is public domain
 %
 % Finite probability spaces
\begin{defproblem}{weightedcoin}
\begin{onlyproblem}%
A coin is weighted so that heads is four times as likely
as tails. Find the probability that:
\begin{textenum}
\item tails appears,
\item heads appears
\end{textenum}
\end{onlyproblem}
\begin{onlysolution}%
Let $p=P(T)$, then $P(H)=4p$. We require $P(H)+P(T)=1$,
so $4p+p=1$, hence $p=\frac{1}{5}$. Therefore:
\begin{textenum}
\item $P(T)=\frac{1}{5}$,
\item $P(H)=\frac{4}{5}$
\end{textenum}
\end{onlysolution}
\end{defproblem}

\begin{defproblem}{validprobspaces}
\begin{onlyproblem}%
Under which of the following functions does
$S=\{a_1,a_2\}$ become a probability space?
\par
\begin{textenum}
\begin{tabular}{ll}
\item $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$
&
\item\label{validprobspacescorrect1} $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$
\\
\item\label{validprobspacescorrect2} $P(a_1)=1$, $P(a_2)=0$
&
\item $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$
\end{tabular}
\end{textenum}
\end{onlyproblem}%
\begin{onlysolution}%
\ref{validprobspacescorrect1} and \ref{validprobspacescorrect2}%
\end{onlysolution}
\end{defproblem}
\endinput
%%
%% End of file `prob-probspaces2.tex'.
