I've taught Monty hall for ages. It is hard to get it across to everyone. But one trick I have found useful for advanced students is to increase the number of doors. here goes.
Suppose there are 1000000 doors altogether. One has a prize, the rest goats. You pick a door--say number 25. Monty hall then opens door, 1,2,3,4,5,6,...,24,26,27,28,....
up to 324786 which he skips, then he continues opening doors up to one million. So, the choice is now between:
door 25 which you picked
door 324786 which Monty picked.
Most peoples view of symetry breaks down here. Some how, the door Monty picked is much more special than the door we picked.
As an aside, I have sometimes taught that 1/2 is the right answer. THis is easy to motivate if you make it into a two player game. Monty's utility is to confuse the contestent. In other words, he wants the croud to be screaming 1/2 for switch and 1/2 for stay. So what strategy should he use? Basically one that only optionally opens doors so that the final conditional probability is .5.
Finally, a fun simulation that I've done in class is on finance. It is about the only example I know of where variance is the one true answer (as apposed to standard deviation). I've written it up for your sister in name journal, "american statistician". I've a on line link of:
posted by Dean Foster
August 19, 2008
"Penguins are 10 times older than humans and have been here for a very, very long time," said Daniel Ksepka, Ph.D., a North Carolina State University research assistant professor. Dr. Ksepka researches the evolution of penguins and how they came to inhabit the African continent.
Because penguins have been around for over 60 million years, their fossil record is extensive. Fossils that Dr. Ksepka and his colleagues have discovered provide clues about migration patterns and the diversity of penguin species.
to view all of our Pizza Lunch Podcasts!
A free daily summary of the latest news in scientific research. Each story is summarized concisely and linked directly to the original source for further reading.
An early peek at each new issue, with descriptions of feature articles, columns,
and more. Every other issue contains links to everything in the latest issue's table of contents.
News of book reviews published in
and around the web, as well as other noteworthy happenings in the world of science books.
To sign up for automatic emails of the
Update and Scientists' Nightstand issues, create an
online profile, then sign up in the
My AmSci area.