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\begin{document}

\noindent
{\Large 
Probability Worksheet \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~202 \\
Spring Semester 2004}
\vspace{.25in}

\noindent
{\bf WARNING:}  You must {\bf SHOW ALL OF YOUR WORK}.  You will receive 
NO CREDIT if you do not show your work.

\noindent
{\bf DUE:} {\bf TUESDAY, 02 MARCH 2004} 
\begin{enumerate} 
\item M\&M's -- Experiment 1
	\begin{enumerate}
	\item Each student should select one M\&M from his or her bag of
	M\&M's. 
	As a class we have now conducted \spc experiments.  Use
	these experiments to answer the following questions. 
		\begin{enumerate}
		\item What is the empirical probability of selecting a
		yellow M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting a
		red M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting an
		orange M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		blue M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		brown M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		green M\&M from a bag of M\&M's? 
		\end{enumerate}
	\item Each student should replace the M\&M he or she selected.
	Then he or she should select another M\&M.
	As a class we have now conducted \spc experiments.  Use
	these experiments to answer the following questions. 
		\begin{enumerate}
		\item What is the empirical probability of selecting a
		yellow M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting a
		red M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting an
		orange M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		blue M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		brown M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		green M\&M from a bag of M\&M's? 
		\end{enumerate}
	\item Each student should perform the experiment three more times.
	As a class we have now conducted \spc experiments.  Use
	these experiments to answer the following questions. 
		\begin{enumerate}
		\item What is the empirical probability of selecting a
		yellow M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting a
		red M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting an
		orange M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		blue M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		brown M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		green M\&M from a bag of M\&M's? 
		\end{enumerate}
	\item Each student should perform the experiment a total of twenty
	times.  As a class we have now conducted \spc experiments.  Use
	these experiments to answer the following questions. 
		\begin{enumerate}
		\item What is the empirical probability of selecting a
		yellow M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting a
		red M\&M from a bag of M\&M's?  
		\item What is the empirical probability of selecting an
		orange M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		blue M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		brown M\&M from a bag of M\&M's? 
		\item What is the empirical probability of selecting a
		green M\&M from a bag of M\&M's? 
		\end{enumerate}
	\item What is the empirical probability of selecting a red M\&M or
	a yellow M\&M?
	\item What is the empirical probability of selecting a red M\&M and
	a yellow M\&M?  Are these events mutually exclusive.
	\item The M\&M web site contains information on the actual
	color distribution of M\&M's?  How do our results compare with this
	distribution?  
	\item Discuss the Law of Large Numbers in relation to our
	experiments.
	\end{enumerate}
\item M\&M's -- Experiments 2 and 3
	\begin{enumerate}
	\item Experiment 2 --
	Each student should select two M\&M's from their bag of
	M\&M's.  Be sure to select the M\&M's one at a time.  
	Replace the first M\&M before selecting the second.
		\begin{enumerate}
		\item  Conduct this experiment ten times and record your
		results.  (You will conduct ten experiments here.  You
		should replace the M\&M's between each experiment.)  
		\item What is the empirical probability that the first and
		second M\&M's you select will be red?
		\item What is the empirical probability that the first and
		second M\&M's a member of this class selects will be red?
		Are these events independent?
		\item What is the empirical probability that the first M\&M
		you select will be blue and second will be green?
		\item What is the empirical probability that the first M\&M
		a member of this class selects will be blue and second will be 
		green?
		Are these events independent?
		\end{enumerate}
	\item Experiment 3 --
	Each student should select two M\&M's from their bag of
	M\&M's.  Be sure to select the M\&M's one at a time.  Do not
	replace the first M\&M before selecting the second.
		\begin{enumerate}
		\item  Conduct this experiment ten times and record your
		results.  (You will conduct ten experiments here.  You
		should replace the M\&M's between each experiment.  That
		is, you should select on M\&M.  Do not replace it.  You
		should then draw a second M\&M.  Record your results for
		the first and second M\&M's.   Now put both M\&M's back in
		the bag since you have completed the first experiment.
		Proceed to conduct the second experiment.)
		\item What is the empirical probability that the first and
		second M\&M's you select will be red?
		\item What is the empirical probability that the first and
		second M\&M's a member of this class selects will be red?
		Are these events independent?
		\item What is the empirical probability that the first M\&M
		you select will be blue and second will be green?
		\item What is the empirical probability that the first M\&M
		a member of this class selects will be blue and second will be 
		green?
		Are these events independent?
		\end{enumerate}
	\end{enumerate}
\item Let $A$ be the event that a person selected at random has blonde
hair.  Let $B$ be the event that a person selected at random has brown
eyes.  Are these events independent?  Justify your answer.
\item Do numbers 5,6,7,9,14, and 15 in section 10.1 of your textbook.
\item What is The Addition Principle of Counting?  Use a Venn diagram to
explain this principle.
\item Cards.
	\begin{enumerate}
	\item What is the sample space for drawing a card from an ordinary
	deck of cards?
	\item In how many ways can you select a black card or a ten?
		Are these events mutually exclusive?
	\item In how many ways can you select a two or a five?
		Are these events mutually exclusive?
	\end{enumerate}
\item Dice
	\begin{enumerate}
	\item What is the sample space for rolling two dice?
	\item In how many ways can you roll a seven or five?  
		Are these events mutually exclusive?
	\item In how many ways can you roll the dice so that the score is
	seven or at least one of the dice shows a two?
		Are these events mutually exclusive?
	\end{enumerate}
\item There are twenty-four students in this class.
	\begin{enumerate}
	\item In how many ways can we select a President, a Vice President,
	a Treasurer, and a Secretary for this class?
	\item In how many ways can we select a four-member social committee
	for this class?  How is this problem related to the previous
	problem?
	\end{enumerate}
\item Amy, Bailey, and Charles are going to be the 2004 class officers for
the Senior Class at Northrop High School.  One of them will be the
president, another the vice president, and the third will be the treasurer. 
	\begin{enumerate}
	\item Draw a possibility tree to determine all the possible outcomes
	for the 2004 class officers.
	\item Suppose that Charles cannot be the class Treasurer.
	Draw a possibility tree to determine all the possible outcomes
	for the 2004 class officers in this case.
	\end{enumerate}
\item Do numbers 1--12, and 15--19 in section 10.2 of your textbook.
\item In the article ``The Worlds 10 Worst Dictators'' (February 22,
2004), they state that in Equatorial Guinea ``the per capita income is
\$4500 a year,'' but ``60\% of the people live on less than \$1 a day.''
How does this statement relate to our study of statistics?  Would say that
the mean is always a good indicator of the typical value of a set of data?
\item Do numbers 1--8, 10, 11abc, and 12--15 in section 10.3 of your textbook.
\item Do numbers 18 and 19 in section 10.2 of your textbook.
\end{enumerate}
\end{document}
