Wednesday, April 9, 2008

The Monty Hall Probability Problem in the News

It is not every day that a famous probability problem is in the news. John Tierney of the New York Times has written a piece about the economist, Dr. M. Keith Chen's challenge to the traditional interpretation of a cognitive dissonance experiment with monkeys. The graphics in this article are especially good. I had to go looking for this piece since Dr. Chen was not given enough time on CBC's "As it Happens" to actually finish explaining his work. Dr. Chen asserts that the researchers made an error analogous to the one that many people make when faced with the Monty Hall problem.

The long-running game show "Let's Make a Deal" debuted in December 1963 and ran until 1977. The famous Canadian host, Monty Hall, played one game in which the contestant was presented with three doors, numbered 1, 2 and 3.

Behind one of the doors was a fantastic prize, like a car, and behind the other two were booby prizes, like goats. After the contestant chose a door, but before the door was opened, Monty sometimes would have another door opened to expose a booby prize. Although Monty never allowed it, people have speculated about what a contestant should do if they were permitted to switch their choice to the other unopened door. In fact, thousands of letters were received by Parade magazine, including some from professional mathematicians, denouncing the assertion in the "Ask Marilyn" column that the contestant would be better off to switch. This probability problem has become known as the “Monty Hall problem”.

There are lots of simulations and explanations on the web. If you buy the book I co-authored, you can even create a simulation in Fathom.

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