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authorKarl Berry <karl@freefriends.org>2008-09-08 00:42:04 +0000
committerKarl Berry <karl@freefriends.org>2008-09-08 00:42:04 +0000
commit036469499e69e21110bdbbd77af3e90de86a382a (patch)
tree34d517f0b3490d8eed24f45e7bd1ce7ab63ab825 /Master/texmf-dist/doc/latex/probsoln/samples/probspaces.tex
parent2f2e79372e149e87d92bdd0d33d596793e6b1252 (diff)
probsoln 3.0 (27aug08)
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+ % 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}
+}