The Car/Goat (Monty Hall) Problem
This is an interesting problem with a counter-intuitive answer, which
serves as an illustration of Bayes' Rule.
In class (on 2/3/03)
I distributed a copy of an article by Leonard Gillman, ``The
Car/Goats Fiasco'' that appeared in the newsletter of the Mathematical
Association of America. The article was prompted by a column by
Marylin vos Savant discussing the problem and subsequent reader
responses, from both lay people and university professors.
Aside from stating the car/goats problem in a precise from, the
article also contained a related problem concerning the differences
between rates of disagreement in the responses from the general public
and those coming from universities, which can be analyzed
within the same framework as the car/goats problem.
Here are handouts relating to these two problems.
- The Car/Goats Problem (pdf file)
This is the green handout I distributed in class (on 2/5/03)
which contains a precise statement of the problem, with all
assumptions made explicit. This is the version of the problem that I
worked out in detail in class on 2/5/03,
within the conditional probability/Bayes rule framework.
The solution is available under this
link.
- The "Professors versus General Public"
Problem (pdf file). This handout, also distributed on class
on 2/5/03, contains a statement and a complete solution of the
problem mentioned above that appeared in Gillman's article.
Java simulations and background articles
Here are two websites containing simulations of the car/goat problem.
- A java
simulation. This is taken from a cryptography class at UCSD.
Has great graphics.
-
Another java simulation, from a different site at UCSD.
It doesn't have the fancy graphics of the ahove
simulation, but it allows you to play a large number of simulated
games.
-
New York Times article.
This interesting article describes the history of the problem, and
a simulation performed at the home of Monty Hall himself, in which 4
out of 10 games with no switching resulted in a win, but 8 out of 10
games played under the switching strategy lead to a win.
Math 361 X1 Homepage
Math 308 B1 Homepage