From 3a4e9615f8609c9f1f1ad2f2305b6c268ccc657a Mon Sep 17 00:00:00 2001 From: Mark Date: Sun, 14 Jan 2024 19:01:32 -0800 Subject: [PATCH] Removed bad warm-up --- Misc/Warm-Ups/parking.tex | 84 --------------------------------------- 1 file changed, 84 deletions(-) delete mode 100755 Misc/Warm-Ups/parking.tex diff --git a/Misc/Warm-Ups/parking.tex b/Misc/Warm-Ups/parking.tex deleted file mode 100755 index 33a4857..0000000 --- a/Misc/Warm-Ups/parking.tex +++ /dev/null @@ -1,84 +0,0 @@ -\documentclass[ - solutions, - shortwarning, - singlenumbering, - nopagenumber, - nowarning -]{../../resources/ormc_handout} -\usepackage{../../resources/macros} -\geometry{top = 20mm} - -\title{Warm-Up: Parking Problems} -\subtitle{Prepared by \githref{Mark} on \today.} - -\begin{document} - - \maketitle - - - - \problem{A Minor Inconvenience} - A group of eight friends goes out to dinner. Each drives his own car, checking it in with valet upon arrival. - Unfortunately, the valet attendant forgot to tag the friends' keys. Thus, when the group leaves the restaurant, - each friend is handed a random key. - \begin{itemize} - \item What is the probability that everyone gets the correct set of keys? - \item What is the probability that each friend gets the wrong set? - \end{itemize} - - \vfill - - - \problem{Bimmer Parking} - A parking lot has a row of 16 spaces, of which a random 12 are taken. \par - Ivan drives a BMW, and thus needs two adjacent spaces to park. \par - What is the probability he'll find a spot? - - \vfill - \pagebreak - - - \problem{Petty Bruins in Westwood} - Suppose 6 students live on a one-way street which features six parallel parking spaces. - Each student has their favorite spot, and will always check if that spot is free. - If it is, they will park there. If it isn't, they will take the next free spot. - Backing up is not an option. - - If each student chooses a \say{favorite} spot independently and at random...\par - \begin{itemize} - \item what is the probability that each student has a different favorite spot? - \item what is the probability that all six people will park successfully? - \end{itemize} - - - - \vfill - - - - \problem{Ship Packing} - A certain harbor services ships that are exactly 10 meters long. - These ships are equipped with transverse thrusters, and thus have - no problem parking in parallel (a ship may fit in any gap that is - at least 10 meters long). - - \vspace{2mm} - - There is an empty 100-meter span where these ships may be parked in parallel. - Parking spaces are not marked---ships may pick a parking spot anywhere on this - continuous 100-meter length. - - \vspace{2mm} - - As ships arrive, they pick a random available spot along this span. \par - How many ships do we expect to fit on this 100-meter region? - - \hint{This problem is difficult, start with simpler cases.} - - - - \vfill - \pagebreak - - -\end{document} \ No newline at end of file