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author | Karl Berry <karl@freefriends.org> | 2008-09-08 00:42:04 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2008-09-08 00:42:04 +0000 |
commit | 036469499e69e21110bdbbd77af3e90de86a382a (patch) | |
tree | 34d517f0b3490d8eed24f45e7bd1ce7ab63ab825 /Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex | |
parent | 2f2e79372e149e87d92bdd0d33d596793e6b1252 (diff) |
probsoln 3.0 (27aug08)
git-svn-id: svn://tug.org/texlive/trunk@10474 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex b/Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex new file mode 100644 index 00000000000..48f7c3c53d8 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex @@ -0,0 +1,31 @@ + % Finite probability spaces +\newproblem{weightedcoin}{% +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}}{% +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}} + +\newproblem*{validprobspaces}{% +Under which of the following functions does +$S=\{a_1,a_2\}$ become a probability space? +\par +\begin{textenum} +\begin{tabular}{ll} +\incorrectitem $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$ +& +\correctitem $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$ +\\ +\correctitem $P(a_1)=1$, $P(a_2)=0$ +& +\incorrectitem $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$ +\end{tabular} +\end{textenum} +} |