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\title{Problem Set 06}
% YOUR NAME GOES HERE under Author
\author{Your Name}
\maketitle

\begin{enumerate} %(

\item How many ways are there to get either a pair of Kings (exactly 2
kings) or a 3-of-a-kind of Aces (or both the King pair and the Ace
trio) with a standard poker hand?  (For this exercise, a full house
with a pair of Kings counts as a pair of Kings, but 3 (or 4) Kings
doesn't count as a pair of kings, and 4 Aces doesn't count as a
3-of-a-kind.)

% Answer below this line.


\item In the expansion for $(A+B)^{114}$, what constant is in front of
the term $A^{62} B^{52}$?

% Answer below this line.


\item Every pack of Starburst\copyright~ candy has 3 Cherry, 3 Strawberry, 3
Orange and 3 Lemon flavored Starbursts.  In our class, 4 people like
Cherry the best, 13 people prefer Strawberry, 8 prefer Orange, and 2
prefer Lemon.  What is the minimum number of packs of Starbursts I
would need to get so that I could divide the Cherry Starbursts evenly
among those who prefer Cherry, the Lemon Starbursts evenly among those
who prefer Lemon, etc.?

% Answer below this line.


\item If I roll 5 standard 6 sided dice, what are the odds that their
sum will be 7 or fewer?

% Answer below this line.


\item
The incidence of Huntington's disease (an unfortunate genetic
disorder) is about 1 in 15,000.  There are usually no visible signs
for this disease until a person is in their late 30s or early 40s.
There is a test for this disease which has a 1.8\% false positive rate
(i.e., $P\lx(TestPositive\lx(x\rx)|\sim Huntington\lx(x\rx)\rx) =
0.018$ where $TestPositive\lx(x\rx)$ means that person $x$ gets a
positive for the Huntington's test, and $Huntington\lx(x\rx)$ means
that a person actually has Huntington's disease).  If a person has
Huntington's, the test result will be positive virtually 100\% of the
time (i.e.\ $P\lx(TestPositive\lx(x\rx) | Huntington \lx(x\rx)\rx) =
1.0$).  Doug was adopted (and therefore we know nothing about
occurrence of Huntington's disease in his biological family), and he
tests positive for Huntington's.
\begin{enumerate} %( 
\item What is the probability that he actually has this disease?

% Answer below this line.


\item BONUS: The gene that is responsible for Huntington's disease
is dominant.  This means that the probability of someone inheriting the
disease is 50\% if exactly one of their parents has the disease (and
100\% in the extremely rare case where both of their parents have the
disease).  Suppose we find out that Doug's biological father is a
carrier of this gene, but his biological mother isn't.  Given that
Doug's test result is positive, what is the probability that he
has Huntington's disease?

% Answer below this line.


\end{enumerate} %)
\end{enumerate} %)
\end{document} %)