Math 180 Fall 2007
Homework 1

These are just a couple of problems to get you thinking about the first class and warm you up for the semester.
Please write up your solutions neatly and make sure your name is written on top.

Due Tuesday, September 11 (at the beginning of class)

  1. You are considering buying some insurance against a potential loss of $20,000. You expect that there is a 50% probability that you will suffer the loss, and a 50% chance you will stay at your current wealth. Calculate the expected value of the loss to help determine how much you should pay for insurance.

  2. Let's win some money!! You can choose to play one of two games. Each game costs one dollar to play.

    Game 1:
    A wheel with three numbers on it--zero, one, and two--is spun so that there is a 40% chance that the wheel lands on zero, a 10% chance the wheel lands on one, and a 50% chance the wheel lands on two. You get back the amount in dollars of the number that the wheel lands on.

    Game 2:
    A different wheel with three numbers on it--zero, one, and two--is spun so that there is a 5% chance that the wheel lands on zero, a 80% chance the wheel lands on one, and a 15% chance the wheel lands on two. You get back the amount in dollars of the number that the wheel lands on.

    (a) What is the expected amount of money that you will get back from Game 1? What is the expected amount of money that you will get back from Game 2? (Don't forget to answer both of these questions.)

    (b) If you played these games every second of every day for the rest of your life, which statement is most likely to be true: a) you will make more money playing Game 1; (b) you will make more money playing Game 2; or, (c) you will make the same amount of money playing either game. Justify your answer in two or less sentences.