


\textwidth 6.5in\oddsidemargin 0in \textheight 9in\topmargin -0.5in

\pagestyle{myheadings}
\markright{Math 104 Fall 1999, Exam2}


\newcommand{\nan}{\hspace{0.18 in}}
\newcommand{\nln}{\vspace{0.2 in}}
\newcommand{\snln}{\vspace{0.1 in}}
\newcommand{\nc}{\hspace{0.85 in}}
\newcommand{\ssl}{\\[10pt]}


\begin{document}

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\thispagestyle{empty}
\begin{tabular}{ll}
Math 104 & Name(PRINT!)\underline{\hspace{3 in}} \\
Test 2, October 28, 1999 & Instructor\\
\end{tabular}

\begin{center}

\textbf{\Large{READ THESE DIRECTIONS CAREFULLY!}}
\end{center}

\textbf{When you are told to begin, tear off this page and keep it
under your test.}\\
\textbf{\textsl{You will hand in ONLY this answer page.}}
There are 10 pages of questions. For each question, mark an
\textbf{X} over the one correct answer on this page.
\textbf{DO NOT CIRCLE answers!!} To change an answer, erase
completely or black out the wrong answer and mark an \textbf{X}
over the correct answer. For example, if (b) is the correct answer,
then\\
\begin{quote}
(a) \nan (b) \nan (c) \nan (d) \nan (e) \nan will receive full credit\\
(a) \nan (b) \nan (c) \nan (d) \nan (e) \nan will receive nocredit\\
\end{quote}
You will receive 5 points for each correct answer and 0 points for
each incorrect answer.
\textbf{Pocket calculators are NOT ALLOWED}.
\vspace{0.25 in}

\begin{quote}\begin{tabular}{rr}
\textbf{1.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{11.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{2.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{12.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{3.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{13.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{4.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{14.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{5.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{15.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{6.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{16.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{7.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{17.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{8.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{18.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{9.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{19.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\textbf{10.} (a)\nan (b)\nan (c)\nan (d)\nan (e) & \nc
\textbf{20.}(a)\nan (b)\nan (c)\nan (d)\nan (e) \ssl

\end{tabular}\end{quote}

%\vspace{.3 in}
\begin{quote}\begin{tabular}{|l|}
\hline
I have not violated the Honor Code in any way with regard to this test. \\
\\
Signature \\
\hline
\end{tabular}

\begin{tabular}{|l|l|}
\hline
\\
\nan \nan number wrong times 5 = \nan \nan \nan& \textbf{SCORE:\nan \nan \nan}\\
\hline
\end{tabular}\end{quote}


\vspace{11 in}
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\textbf{1.} A fair coin is tossed independently six times.
What is the probability that the number of "heads" obtained is 

different than the number of "tails"?\\
\begin{quote} \begin{tabular}{lllll}
(a) $\frac{11}{16}$ &
(b) $\frac{5}{16}$ &
(c) $1$ &
(d) $\frac{1}{4}$ &
(e) $\frac{63}{64} $
\end{tabular} \end{quote}

\vspace{3.5 in}
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\textbf{2.} You're playing a card game, with a standard 52-card deck,
in which "one-eyed Jacks" (half of the Jacks are "one-eyed")
and twos are wild cards. You pick two cards at random.
What's the probability that you pick at least one wild card?\\
\begin{quote} \begin{tabular}{lllll}
(a) $\frac{6}{52}$ &
(b) $1 - \left(\frac{46}{52}\right)\left(\frac{45}{51}\right) $ &
(c) $\left(\frac{4}{52}\right)\left(\frac{2}{52}\right) $ &
(d) $\frac{ {{6}\choose{2}} } { {{52}\choose{2}} }$  &
(e) $\left( \frac{6}{52} \right)^2 $ 
\end{tabular} \end{quote}

\vspace{3.5 in}
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\textbf{3.} Suppose a red die and a green die are tossed and the numbers
on the uppermost faces are observed. What's the probability that the
numbers don't add up to 11?\\
\begin{quote} \begin{tabular}{lllll}
(a) $\frac{17}{18}$ &
(b) $\frac{11}{36}$ &
(c) $\frac{11}{12}$ &
(d) $\frac{1}{18}$ &
(e) $\frac{35}{36}$ 
\end{tabular} \end{quote}

\vspace{3.5 in}
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\textbf{4.} Let $E$ and $F$ be independent events with $P(E) = 0.2$
and $P(F) = 0.5$. Find $P(E\cup F)$\\
\begin{quote} \begin{tabular}{lllll}
(a) $0.7$ &
(b) $0.1$ &
(c) $0.8$ &
(d) $1$ &
(e) $0.6$ 
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{5.}  Given that $P(E\cap F') = \frac{1}{5}$, 
$P(E) = \frac{1}{2}$ and $P(F) = \frac{2}{5}$, find $P(E'\vert F)$\\
\begin{quote} \begin{tabular}{lllll}
(a) $\frac{1}{5}$ &
(b) $\frac{1}{2}$ &
(c) $\frac{1}{4}$ &
(d) $\frac{3}{4}$ &
(e) $\frac{2}{5}$ 
\end{tabular} \end{quote}

\vspace{4  in}
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\textbf{6.} The probability of Derek Jeter hitting a homerun is 
$0.1$ if there is no one on base, and 
$0.2$ if there is at least one person on base.
The probability of no one being on base when it's Jeter's turn to bat
is $0.7$. What percentage of the time does Jeter hit a homerun?\\
\begin{quote} \begin{tabular}{lllll}
(a) $2\%$ &
(b) $6\%$ &
(c) $7\%$ &
(d) $13\%$ &
(e) $15\%$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{7.} A fair coin is tossed three times and you are told that
"heads" has come up at least once. What is the probability that
all three tosses were heads?\\
\begin{quote} \begin{tabular}{lllll}
(a) $\frac{1}{4}$ &
(b) $\frac{1}{8}$ &
(c) $\frac{1}{7}$ &
(d) $\frac{2}{3}$ &
(e) $\frac{1}{2}$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{8.} Three airlines carry all flights into Jabip. 
Information about the airlines and their on-time record is given below.
If a plane arriving in Jabip is late, what's the 
probability that the plane is from Airline B?\\
\begin{quote} \begin{tabular}{|c|c|c|}
\hline
Airline & percentage of flights & probability of delay \\
\hline
A & $50\%$ & $1/50$ \\
\hline
B & $30\%$ & $1/20$ \\
\hline
C & $20\%$ & $1/40$ \\
\hline
\end{tabular} \end{quote}

\begin{quote} \begin{tabular}{lllll}
(a) $\frac{3}{7}$ &
(b) $\frac{1}{8}$ &
(c) $\frac{3}{10}$ &
(d) $\frac{1}{3}$ &
(e) $\frac{1}{2}$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{9.} An urn contains 5 red balls and 2 white balls. 
Balls are drawn from the urn at random, one at a time without replacement,
until a white ball is drawn. What is the probability of drawing the
white ball on the third drawing?\\
\begin{quote} \begin{tabular}{lllll}
(a) $\frac{4}{21}$ &
(b) $\frac{ {{7}\choose{2}} } { {{7}\choose{4}} }$  &
(c) $\frac{ {{7}\choose{3}} } { {{7}\choose{4}} }$  &
(d) $\frac{2}{7}$ &
(e) $\frac{1}{14}$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{10.} Six people with June birthdays are randomly chosen.
What is the probability that at least two of them have the same birthday?

(There are 30 days in June!)\\


\begin{quote} \begin{tabular}{lllll}
(a) $\frac{6}{30}$ &
(b) $1 - \left( \frac{6}{30}\right)^6 $ &
(c) $1 - \frac{30\cdot 29\cdot 28\cdot 27\cdot 26\cdot 25}
{ {{30}\choose{6}} }$ &
(d) $1 - \frac{29\cdot 28\cdot 27\cdot 26\cdot 25}{30^5}$ &
(e) $\left( \frac{5}{6}\right)^6$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{11.} The US Senate voted on a particular bill, for which the
results are shown in the table (Abstain = did not vote).
A Senator is selected at random (from the 100 Senators) and found
to have voted "Yes". What's the probability that he/she is a democrat?\\

\begin{quote} \begin{tabular}{|c|c|c|c|}
\hline
Affiliation & Yes & No & Abstain \\
\hline
Democrat & 3 & 34 & 3 \\
\hline
Republican & 57 & 2 & 1 \\ 
\hline
\end{tabular} \end{quote}

\begin{quote}\begin{tabular}{lllll}
(a) $\frac{2}{5}$ &
(b) $\frac{1}{20}$ &
(c) $\frac{3}{40}$ &
(d) $\frac{2}{3}$ &
(e) $\frac{3}{100}$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{12.} A basketball player makes $75\%$ of her free throws.
If she takes three independent shots, what's the probability that
she makes at least one?\\
\begin{quote}\begin{tabular}{lllll}
(a) $\frac{3}{5}$ &
(b) $\frac{63}{64}$ &
(c) $\frac{27}{64}$ &
(d) $\frac{1}{4}$ &
(e) $\frac{3}{4}$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{13.} You bought 4 new tires for your car. Of the particular model
you bought, $0.1\%$ of the tires made are defective. What's the probability
that at least one of the tires you bought is defective?\\
\begin{quote}\begin{tabular}{lllll}
(a) $0.0001$ &
(b) $1 - \left(\frac{1}{1000}\right)^4$ &
(c) $0.001$ &
(d) $1 - (0.999)^4$ &
(e) $1 - (0.9)^4$ 
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{14.} The table below shows the percents of total output
and of defective output for four factories of computer monitors.
A monitor is selected at random from the output and found to be
defective. Which factory is most likely to have produced it?\\
\begin{quote} \begin{tabular}{|c|c|c|}
\hline
Factory & percent of total output & percent of defectives \\
\hline
A & $10\%$ & $30\%$ \\
\hline
B & $20\%$ & $15\%$ \\
\hline
C & $30\%$ & $10\%$ \\
\hline
D & $40\%$ & $10\%$ \\
\hline
\end{tabular} \end{quote}

\begin{quote}\begin{tabular}{lllll}
(a) A &
(b) B &
(c) C &
(d) D &
(e) None of the above
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{15.} Edie Brickell goes to the market for some milk. 
In the cooler, there are 15 cartons of milk, of which 5 (randomly
positioned) cartons have exceeded their expiration dates. 
She will examine the cartons one at a time and buy the first good
one she finds. Of course, she won't examine the same carton twice.
Furthermore, being in a big hurry, she only has time to examine
at most three cartons, so she could leave without buying any milk.
What is the probability that she will leave without buying any milk?\\

\begin{quote}\begin{tabular}{lllll}
(a) $\frac{2}{91}$ &
(b) $\frac{1}{3}$ &
(c) $\frac{1}{27}$ &
(d) $\frac{1}{8}$ &
(e) $1 - \left( \frac{5}{15}\right)^3$
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{16.} A student takes a True-False exam with 8 questions
and guesses all answers (since he is guessing anyway, he will answer
either true or false for every question). Which of the following
has the lowest probability?\\
\begin{quote}
$A$ = "the student correctly answers less than half of the questions"\\
$B$ = "the student correctly answers exactly half of the questions"\\
$C$ = "the student correctly answers more than half of the questions"\\
\end{quote}

\begin{quote}\begin{tabular}{lllll}
(a) $A$ &
(b) $B$ &
(c) $C$ &
(d) $P(A)$ and $P(C)$ are equal and lowest &
(e) all 3 are equal
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{17.} Three cards are drawn from a standard 52-card deck
(without replacement).
What is the probability that all three are of the same suit
(the suits are Clubs, Spades, Diamonds and Hearts)?\\

\begin{quote}\begin{tabular}{lllll}
(a) $1 - \frac{ {{13}\choose{3}} }{ {{52}\choose{3}} }$ &
(b) $\left( \frac{1}{4}\right)^3$ &
(c) $1 - \left( \frac{3}{4} \right)^3$ &
(d) $4 \frac{ {{13}\choose{3}} }{ {{52}\choose{3}} }$ &
(e) $\frac{1}{12}$ 
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{18.} A particular company estimates that $2\%$ of it's
employees are using illegal drugs. They decide to implement a
random drug-testing program. However, being a company of limited
means, they opt to use an inexpensive test with the following
characteristics: \\
1) The result of the test is always either positive or negative (i.e.,
never both and never inconclusive)\\
2) Of the people using drugs, $95\%$ of them will
test positive. \\
3) Of the people not using drugs, $90\%$ of them will
test negative.\\
Somebody tests positive for drug use, and the manager
(never having taken this course) immediately fires that person. 
What is the probability that the person was \textbf{not} using drugs?\\

\begin{quote}\begin{tabular}{lll}
(a) $0.1$ \nan $(10\%)$  &
(b) $\frac{0.1}{0.98}$ \nan $(\approx 10.2\%)$ &
(c) $0.002$ \nan $( 0.2\%)$ \\ \\
(d) $\frac{0.019}{0.117}$ \nan $(\approx 16\%)$ &
(e) $\frac{0.098}{0.117}$ \nan $(\approx 84\%)$ &
\end{tabular} \end{quote}

\vspace{4 in}
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\textbf{19.} You have a box containing 10 batteries, but 6 of them
are known to be bad (although you don't know which six). You select
two batteries at random to put in your remote control (which will not
work unless it has two good batteries). What is the probablity
that, after putting the selected batteries in the remote control, it 
will not work?\\

\begin{quote}\begin{tabular}{lllll}
(a) $\frac{4}{25}$ &
(b) $\frac{4}{10}\cdot \frac{3}{9}$ &
(c) $\frac{2}{15}$ &
(d) $\frac{2}{5}$ &
(e) $\frac{13}{15}$
\end{tabular} \end{quote}

\vspace{4 in}

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\textbf{20.} Two letters are chosen at random from your instructor's
last name, with replacement.
What is the probability that one of them is the letter 'i'
given that at least one of them is a vowel?\\
\begin{quote}\begin{tabular}{lllll}
(a) $\frac{1}{3}$ &
(b) $\frac{2}{9}$ &
(c) $\frac{ 6 }{ {{7}\choose{2}} }$ &
(d) $\frac{ 5 }{ {{6}\choose{2}} }$ &
(e) $\frac{7}{33}$
\end{tabular} \end{quote}

\vspace{4 in}
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\end{document}



