Group Homework, November 8, 2001

This homework is due on November 19th. You may work in groups of up to three. The more members in your group the higher quality of work I will expect. You must choose one of the problems below. You answers should be either carefully and very neatly handwritten, or typed. Tables of data with a few sample calculations would be ideal. You should also write in coherent sentences a description of how the work was done and any answers to questions that I asked below. I will slash points for sloppy work.

This will be worth 30 quiz points.

Project One

Find fifteen different state or national lottery games. Describe the lottery games and then determine how many possible tickets there are. If you have to pay 45% of all winnings to the IRS determine how high the jackpot would need to be before it would pay off to buy every ticket.

For one of the lotteries, concoct a harebrained scheme that would enable you to buy every ticket in one week assuming that one person can buy five tickets every two minutes. How many people would you need, etc.

Project Two

Law Enforcement officials have long complained about the growing number of license plates that make it difficult for them to identify what state a car is from. You are going to devise a method that makes the color scheme irrelevant.

For instance, one state could use four letters and a digit (AAAA0) and another two letters and three digits (AA000).

Assuming that we want only a combination of five digits or letters on a plate (I know that most plates have more than this) and that each car is issued a standard license plate, create a system for each of the ten states below that generates enough plates for the cars they have and is unique for each state.

State	Cars
Maine	650000
Massachusetts	3150000
Connecticutt	1700000
New York	9970000
New Hampshire	600000
Vermont	300000
New Jersey	420000
Rhode Island	502000
Delaware	390000
Maryland	2650000

Project Three

You are visiting Atlantic City and are playing video poker. You have drawn the following five cards $( \clubsuit A - \clubsuit Q - \clubsuit J - \clubsuit 10 - \diamondsuit 9)$. You have six possible plays given this hand. You can discard any single card in your hand or hold on to what you have. Given the cards you have, here are the possible winning hands and their payouts.

List of possible hands and their payoff

• Straight - Five consecutive cards, such as 2, 3, 4, 5, and 6. They need not be of the same suit. An Ace can be used in two ways. It can be a "1" card in a A, 2, 3, 4, 5 hand, or it can also be placed above the King in an 10, J, Q, K, A sequence. ($4)
• Flush - Five cards of the same suit. They do not have to be in any order. ($6)
• Royal Flush - The best possible hand in poker. You'll rarely ever see this hand. It is an A, K, Q, J, and 10, all in the same suit. ($250)

Determine the best card to discard, if any. Back up your strategy with calculations of the probability of different events. You should assume the next card you get could be any of the 47 cards remaining.

Remember: Life is a story problem.