Chance at Dartmouth Fall 1994

Chance at Dartmouth Fall 1994

The CHANCE Project

Version 0.1
21 September 1994


This document consists of the collection of handouts for a CHANCE course being taught at Dartmouth College during the Fall 1994 term by Peter Doyle, Laurie Snell, and Jeanne Albert.

Course Description


Welcome to Chance!

Chance is an unconventional math course. The standard elementary math course develops a body of mathematics in a systematic way and gives some highly simplified real-world examples in the hope of suggesting the importance of the subject. In the course Chance, we will choose serious applications of probability and statistics and make these the focus of the course, developing concepts in probability and statistics only to the extent necessary to understand the applications. The goal is to make you better able to come to your own conclusions about news stories involving chance issues.

Topics that might be covered in Chance include:

During the course, we will choose six to ten separate topics to discuss with special emphasis on topics currently in the news. We will start by reading a newspaper account of the topic. In most cases this will be the account in the New York Times. We will read other accounts of the subject as appropriate, including articles in journals like Chance, Science, Nature, and Scientific American, and original journal articles. These articles will be supplemented by readings on the basic probability and statistics concepts relating to the topic. We will use computer simulations and statistical packages to better illustrate the relevant theoretical concepts.


The class will differ from traditional math classes in organization as well as in content: The class meetings will emphasize group discussions, rather than the more traditional lecture format. Students will keep journals to record their thoughts and questions, along with their assignments. There will be a major final project in place of a final exam.

Scheduled meetings

The class meets every during the 10A period (Tuesday and Thursday 10:00 to 11:40) in 13 Silsby. The x-hour will meet every week at 3:00 P.M. in 102 Bradley and will be used for discussion of material in the text, questions about homework, use of the computer, or anything else relating to the course.

Discussion groups

We want to enable everyone to be engaged in discussions while at the same time preserving the unity of the course. From time to time, we will break into discussion groups of 3 people.

Every member of each group is expected to take part in the discussion and to make sure that everyone is involved: that everyone is being heard, everyone is listening, that the discussion is not dominated by one person, that everyone understands what is going on, and that the group sticks to the subject.

After a suitable time, we will ask for reports to the entire class. These will not be formal reports. Rather, we will hold a summary discussion between the teachers and reporters from the individual groups.


The required texts for the course are Freedman, Pisani, Purves, and Adhikari, Statistics, 2nd edition and Data Desk by Velleman. They are available at the Dartmouth Bookstore.


Each participant should keep a journal for the course. This journal will include:

A good journal should answer all the questions asked, with evidence that some time has been spent thinking about the questions before answering them. In addition, there should be evidence of original thought: evidence that you have spent some time thinking about things that you weren't specifically asked about. This might take the form of: finding and commenting on news articles about topics relevant to the course; asking us challenging questions; making connections between what went on in class and experiences in your own life; going to a casino and winning a lot of money.

In writing in your journal, exposition is important. If you are presenting the answer to a question, explain what the question is. If you are giving an argument, explain what the point is before you launch into it. What you should aim for is something that could communicate to a friend or a colleague a coherent idea of what you have been thinking and doing in the course.

You are encouraged to cooperate with each other in working on anything in the course, but what you put in your journal should be you. If it is something that has emerged from work with other people, write down who you have worked with. Ideas that come from other people should be given proper attribution. If you have referred to sources other than the texts for the course, cite them.

Your journal should be kept on loose leaf paper. Journals will be collected periodically to be read and commented on. If they are on loose leaf paper, you can hand in those parts which have not yet been read, and continue to work on further entries. Pages should be numbered consecutively and except when otherwise instructed, you should hand in only those pages which have not previously been read. Write your name on each page, and, in the upper right hand corner of the first page you hand in each time, list the pages you have handed in (e.g. [7,12] on page 7 will indicate that you have handed in 6 pages numbered seven to twelve).

Journals will be collected and read as follows:

Thursday 6 October Thursday 20 October Thursday 3 November Thursday 17 November Tuesday 29 November

Homework To supplement the discussion in class and assignments to be written about in your journals, we will assign readings from FPPA, together with accompanying homework. When you write the solutions to these homework problems, you should keep them separate from your journals. Homework assignments will be assigned at each class meeting and should be handed in at the next class meeting.

Final project

We will not have a final exam for the course, but in its place, you will undertake a major project. The major project may be a paper investigating more deeply some topic we touch on lightly in class. Alternatively, you could design and carry out your own study. Or you might choose to do a computer-based project. To give you some ideas, a list of possible projects will be circulated. However, you are also encouraged to come up with your own ideas for projects.

Chance Fair

At the end of the course we will hold a Chance Fair, where you will have a chance to present your project to the class as a whole, and to demonstrate your mastery of applied probability by playing various games of chance. The Fair will be held from during the final examination time assigned by the registrar.


Materials related to the course will be kept on our World Wide Web server and available by Mosaic. In particular this course description and the class assignments can be obtained there. Software for using Mosaic can be obtained from the public file server in the folder Macintosh Software, then Internet Goodies, and finally Searching the Internet. Library Reserve Previous issues Chance magazine can be found on reserve in Kresge Library. Other materials that we will want to put on reserve will be in Baker Library.


Your grade in the course will be determined by your work on journal and class discussion (30%), homework (30%), and final project (40%). Since much of the material we discuss is not contained in text material and is the result of class discussion, a good grade will require regular attendence and participation in the the class.


Assignment 1


Read the New York Times article ``When is a coincidence too bad to be true?" by Gina Kolata and answer the following questions.

Homework assignments for Tuesday September 28

Journal Assignment for Tuesday September 28

Read the article `How numbers can trick you'. See how many examples of these six dealy sins of statistical misrepresentation you can provide.

Assignment 2


Rare events

Read the article DNA fingerprinting; it's a case of probabilities written by Richard Saltus for the Boston Globe and discuss the following questions.

  1. Estimate the probability that you have an identical twin that you do not know about.
  2. Estimate the probability that the DNA evidence in a randomly selected trial has been faked because someone involved wants to get a conviction.
  3. Estimate the probability that someone else has the same social security number as you.
  4. Estimate the probability that someone in the world has at least half of their chromosomes in common with you.

Enough, already

One way to avoid most of the nonsense associated with DNA fingerprinting would be to collect DNA fingerprints of everyone in the country. Then instead of speculating about whether certain genetic markers are independent within subpopulations, and all that hogwash, we can just check a DNA sample against everyone in the population.

Why all the zeroes?

Say you're prosecuting a case where there is a DNA match. It occurs to you that you could ask your experts to testify, not that there is only a one-in-a-billion chance of this match, but rather that the chance is `real small', and while opinions differ about exactly how small that might be, nobody will contest that the chance is bigger than one in a hundred.

It depends

  1. Do you think that women at Dartmouth are more likely to have blond hair than men? How could you decide this?
  2. Name some pairs of characteristics of people that are likely to be independent.
  3. Suppose you wanted to see if ``color of eyes" is independent of ``color of hair". How, using data from this class, could we try to determine this?

Homework assignments for Thursday September 29