Monday, May 16, 2005

The middle-aged Tennessee lady and the Monty Hall problem

You need to read first the previous post for the adventures of the middle-aged Tennessee lady for this post to make more sense.

In the season finale on Numb3rs last week there was a great example of the skill required to make tough concepts understood to a layman. Charlie is supposed to teach the Monty Hall problem in class "math for non mathematicians", where the students are people that have nothing to do with science (in fact, the lesson did not target them; it targeted the tv audience really). It is quite simple to state the problem: there are 3 closed curtains, behind of which there are 2 goats and 1 car. You select a curtain trying to win the car, and after you do that the all mighty host opens one of the other curtains to reveal a goat. Then he asks, do you want to switch you choice (select the 3rd curtain)?. Or, more importantly, does it matter?

The answer to this problem is not of interest here. What matters is seeing from the point of view of the writer of the TV show Numb3rs: he/she has only 30sec (TV time is expensive) to explain to 20,000,000 people watching the show why the answer is the way it is. It took me a while to understand the answer to this problem myself a few months ago, and in 2 different ways, none of which was simple enough (either draw a chart with all possibilities or use probability theory). However in that show, they managed to explain the mechanics of the answer in just 30seconds indeed, giving very carefully crafted arguments in just 3 sentences. It was the simplest explanation of the Monty Hall I have ever seen. This is the type of explanations we should have in any aspect of science (followed by the exact math details of course) - not the complicated O'Brien type of arguments we usually hear. Watch it if you have time - it's a really good piece of the show.