Fall Semester 2002

Lecture Notes Seven: Practice problems for the upcoming exams.
Here's a problem that is very well suited for the practical exam.

1. Consider tossing two fair coins, with payoffs of 1 for a single head and 3/2 for a double head. That is, this is a game in which you toss two coins and you are paid according to the following rule:

Outcome Probability You win
TT 1/4 $0.00
TH 1/4 $1.00
HT 1/4 $1.00
HH 1/4 $1.50

You need to pay $1.00 to participate in each draw. Should you play the game?

2. Similarly there is a game in which you roll 6 dice and you are paid according to the following rule:

if 1 face shows 6 you win $1.00
if 2 faces show 6 you win $1.50
if 3 faces show 6 you win $2.00
if 4 faces show 6 you win $2.50
if 5 faces show 6 you win $3.00
if 6 faces show 6 you win $3.50
You have to pay $1.00 to play. Should you play this game?

The argument (given by the gambler offering you the chance) for why you should play is that you expect that you will get at least one 6 on each roll of 6 dice, and all the higher ones are gains, so that if you pay $1.00 to play then it is favorable to you. But is it? (It is fairly safe to assume that any widely played game is favourable to the person running it and not to the player).

Can you design and run an experiment that clarifies this question?

3. I will have a few more problems posted here for our practice before the exams.

Last updated: Nov 12, 2002 by Adrian German for A113