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\title{Stochastic Processes}
\author{Summer Semester 2026, Exercise 1}
\date{In-class discussion, Tuesday, April 21}
\maketitle

\urldef\urla\url{https://en.wikipedia.org/wiki/Marilyn_vos_Savant#%22Two_boys%22_problem}
\urldef\urlb\url{https://en.wikipedia.org/wiki/Marilyn_vos_Savant#Monty_Hall_problem}
\begin{enumerate}

\item A shopkeeper says she has two new baby beagles to show you, but
she doesn't know whether they're male, female, or a pair. You tell her
that you want only a male, and she telephones the fellow who's giving
them a bath. ``Is at least one a male?'' she asks him. ``Yes!'' she
informs you with a smile. What is the probability that the other one
is a male?\footnote{\urla}

\item A shopkeeper says she has two new baby beagles to show you, but
she doesn't know whether they're male, female, or a pair. You tell her
that you want only a male, and she telephones the fellow who's giving
them a bath. ``Is at least one a male?'' she asks him. ``Yes,
\emph{the one he is holding just now is a male}!'' she informs you
with a smile. What is the probability that the other one is a male?

\item Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say \#1, and the host, who knows what's behind the doors, opens another door, say \#3, which has a goat. He says to you, ``Do you want to pick door \#2?'' Is it to your advantage to switch your choice of doors?\footnote{\urlb}

\item Suppose you're on a game show, and you're given the choice of
three doors. Behind one door is a car, behind the others, goats. You
pick a door, say \#1, and the host, \emph{being unattentive for the
split of a second, slips and accidentally open another door}, say \#3,
which has a goat. He says to you, ``Do you want to pick door \#2?'' Is
it to your advantage to switch your choice of doors?

\end{enumerate}
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