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\def\header{{\hfill Exam 1 \hfill A. Miller \hfill Fall 2003
                                       \hfill Math 210\hfill}}
\markboth\header\header
\newcount\probno
\newcount\total
\newwrite\examTBLFile



\probno=0


\def\prob#1{\advance\probno by 1  \vfill \newpage % \par
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       \string& #1 \string&
       \string\qquad \string\\ \string\hline}}

\def\finishtbl{
    \immediate\write\examTBLFile{Total \string& \the\total
    \string& \qquad \string\\ \string\hline}
     }

%%% \outer\def\answer{ {\par\bigskip Circle your answer.} \par\medbreak

\newwrite\ans
\immediate\openout\ans=answers
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\begin{document}

\bigskip

Show all work.  

Simplify your answers.  

Circle your answer.

\bigskip

No notes, no books, no calculator, no cell phones, no pagers, no
electronic devices. 


\par\vskip .25in
\begin{center}
Name\makebox[3in]{\hrulefill} \\
\end{center}

\bigskip
Circle your Discussion Section:
\begin{verbatim}
       DIS 332   9:55 R 395 VAN HISE            
       DIS 331   9:55 T  52 BASCOM            
       DIS 335 12:05p T 123 INGRAHAM            
       DIS 336 12:05p R 114 INGRAHAM
\end{verbatim}
\bigskip

\begin{center} \Large
 \begin{tabular}{||c|c|c||} \hline\hline
  Problem & Points & Score \\  \hline\hline
   \input{exam.tbl}
  \hline \hline
 \end{tabular}
\end{center}

\immediate\openout\examTBLFile=exam.tbl

\bigskip
 
Solutions will be posted shortly after the exam:
www.math.wisc.edu/$\sim$miller/m210



\setcounter{page}{0}




\newpage 

\prob{5} % 2.1 - 21
Suppose a coin is weighted so that when the coin is flipped the result
is heads 5 times as often as tails.  What probabilities should be
assigned to the outcomes "heads" and "tails"?
\answer \par heads:$5/6$ \par tails:$1/6$

\prob{5} % 1.1 - 11,21
Suppose $A=\{a,b,c\}$ and $B=\{b,d\}$. What is

\bigskip
\par (a) $A\times B$

\vfill

\par (b) $A\cup B$

\vfill

\par (c) $A\cap B$

\vfill

\par (d) $A\cap B'$

\vfill

\answer \par (a) $\{(a,b),(a,d), (b,b),(b,d),(c,b),(c,d)\}$
\par (b) $\{a,b,c,d\}$ 
\par (c) $\{b\}$ 
\par (d) $\{a,c\}$

\prob{5} % 3.3 - 21
There are two buckets, labeled X and Y.  Bucket X contains
1 red and 2 green balls, and bucket Y contains 2 red and 5 green balls.
An experimenter randomly chooses two balls from bucket X and adds 
them to bucket Y.  He then randomly chooses a ball from bucket Y.
What is the probability this ball is red?
\answer $8/27$ 
 
\prob{5} % 3.1 - 21
Each Monday morning Max attends Math210 with probability $1/2$ and
skips Neurobiology302 with probability $2/3$.  He attends both
with probability $1/6$.  What is the probability that he goes
to exactly one of the lectures? 
\answer $1/2$


\prob{5} % 3.2 - 21
Professor Throckmorton has  15 M \& M candies in his pocket.
6 are his favorite blue ones and 9 are green one.  He randomly
reaches into his pocket and chooses 3 candies.  Given that all
three candies he has chosen are the same color what is the probability 
he has chosen all blue candies?
\answer $5/26$

\prob{5} % 2.4 - ?
At a ballroom dance there are 4 girls and 5 boys.  One of the boys
is Mortimer who has a secret crush on one of the girls, Hortense.  At
the end of the lesson the instructor chooses two boy-girl couples
to demonstrate the fox trot.  What is the probability that one
of the couples chosen is Mortimer and Hortense?
\answer $1/10$

\prob{5} % 1.2 -23
Let A and C be sets with $A\subseteq C$. 
Suppose that $n(A)=4$ and $n(C)=12$.  
In how many different ways can you select $B$ so that 
$A\subseteq B$, $B\subseteq C$, and $n(B)=5$?
\answer $8$

\prob{5} % 1.3 - 9
In a survey 50 families, it was found that
26 families had at least one daughter, 32 familes had at
least one son, and 18 had at least one daughter and at least one son. 
How many families had no children?
\answer $10$

\prob{5} % 3.5 - 23
A basketball player makes on average 2 out of every 3 penalty shots.  
How many shots must he take to ensure that he has probabability at least
.95 of making at least one shot?
(Make sure you explain your answer for this one.)

\answer $3$

\prob{5} % 2.3 - 21 
At Taco bell there are 10 ingridients for making burritos including
tortillas, beans, cheese, and seven others.  A burrito is prepared
by combining up to six of these 10 ingridients but always including a
tortilla, beans, and cheese. How many different burritos can Taco
bell sell?  (Note: an ingridient is either chosen or not, no doubling.)
\answer $64$

\prob{5} % 2.2-21
Max is going on a road trip across Wisconsin.  He plans to visit
friends in Beloit, Green Bay, Janesville, Madison, and Wausaw. He
can visit them any order except he must visit Beloit before he
visits Green Bay, because he needs to take something from his friend
in Beloit to his friend in Green Bay.  How many different travel
iternaries can he have?
\answer $60$

\prob{5} % 3.4-25
A forester plants seeds from Oak, Pine, or Walnut trees in his
forest. It is known that a random Oak seed or Pine seed germinates with 
probability $1/2$ while a Walnut seeds germinates with
probability $1/3$.  A new forest has been planted randomly with
$1/3$ Oak, $1/6$ Pine, and $1/2$ Walnut.  A few weeks latter the
forester sees that one of the seeds has germinated.  What is the
probably that this seedling is an Oak?
\answer $2/5$


\finishtbl

\printanswers

\end{document}


