# hw2 - \documentclasscfw_amsart...

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\documentclass{amsart} \usepackage[margin=1in]{geometry} \begin{document} \title{Math 145: Homework 2} \author{Andrew Berget} \maketitle As before, do not hand in [bracketed] problems. This homework is due on Wednesday January 20. \bigskip \textbf{Problem A.} We toss a fair coin $n$ times and get get $h$ heads and $t$ tails where $h>t$ are fixed integers. Your goal in this problem is to prove that \textit{The probability that, as we toss the coin, the number of heads is always larger than the number of tails is equal to $(h-t)/(h+t)$.} For example, if $h=3$ and $t=2$ then the sequences of tosses $HHTHT$ satisfies our condition, but $HTHHT$ does not since at the second toss the number of tails equals the number of heads. \begin{enumerate} \item A walk on the grid of points with integer coordinates that only uses steps that are north-east $\nearrow$ or south-east $\searrow$ is called a \textit{diagonal lattice path}. How many diagonal lattice paths are there from $(0,0)$ to $(u,v)$? (This is essentially

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## This note was uploaded on 11/13/2011 for the course MATH 145 taught by Professor Peche during the Winter '07 term at UC Davis.

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hw2 - \documentclasscfw_amsart...

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