CS5014 Fall 2006 Assignment 11
This assignment should be handed in typed using a word processor such
as LaTeX or Microsoft Word. No handwritten work will be accepted.
Due Thursday, November 2 at the beginning of class
1. [10 points] Navidi Chapter 2, Supplementary Exercise 2.
2. [10 points] Navidi Section 4.9, Exercise 4.
3. [10 points] Navidi Chapter 4, Supplementary Exercise 8.
4. [20 points] You may solve this problem analytically or by
Jack the Gambler has a system. He's going to Las Vegas to try it out.
He observes that a roulette wheel lets him win half the time if he
bets that the result is an even number, and he receives two times his
bet if he wins. So his system works like this: He starts by betting
$1, and he doubles his bet every time he loses. Eventually he must win
with a net profit (for that series of bets) of $1. For example, say he
bets $1 and loses, then $2 and loses, then $4 and wins $8. His net
winnings over the series of 3 bets are $1.
Assume that the roulette wheel will run 60 times/hour. If Jack
plays for two hours (give or take a few minutes to complete the
current cycle), how much should he expect to win?
Unfortunately, Jack has a problem. He's only got $1000 with him.
So if he loses enough times in a row, he's out a lot of money because
he won't have enough money left to continue the cycle!
If this should happen, he will start over with a new cycle (beginning
with a $1 bet) if he has any money left. With this taken into
consideration, how much should he expect to win or lose in 2 hours?
In 20 hours?